Content-Type: multipart/mixed; boundary="-------------0408130835417" This is a multi-part message in MIME format. ---------------0408130835417 Content-Type: text/plain; name="04-250.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-250.comments" PACS-Code: 02.50.Ey, 05.10.Gg, 05.40.-a ---------------0408130835417 Content-Type: text/plain; name="04-250.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-250.keywords" Stochastic resonance, residence-time distribution, noise-induced exit, oscillating barrier, periodic driving, activated escape, metastability, cycling. ---------------0408130835417 Content-Type: application/postscript; name="resid.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="resid.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: resid.dvi %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips resid -o %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2004.08.13:1528 %%BeginProcSet: texc.pro %! 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435.1 l 166.2 434.7 l 166.5 434.3 l 166.8 434 l 167.1 433.6 l 167.4 433.2 l 167.7 432.8 l 168 432.4 l 168.3 432 l 168.6 431.6 l 168.9 431.1 l 169.2 430.7 l 169.5 430.3 l 169.8 429.9 l 170.1 429.4 l 170.4 429 l 170.8 428.6 l 171.1 428.1 l 171.4 427.7 l 171.7 427.2 l 172 426.8 l 172.3 426.4 l 172.6 425.9 l 172.9 425.5 l 173.2 425 l 173.5 424.6 l 173.8 424.1 l 174.1 423.7 l 174.4 423.3 l 174.7 422.8 l 175 422.4 l 175.3 422 l 175.7 421.6 l 176 421.2 l 176.3 420.8 l 176.6 420.4 l 176.9 420 l s n 176.9 420 m 177.2 419.6 l 177.5 419.2 l 177.8 418.9 l 178.1 418.5 l 178.4 418.2 l 178.7 417.9 l 179 417.6 l 179.3 417.4 l 179.6 417.1 l 179.9 416.9 l 180.2 416.7 l 180.6 416.6 l 180.9 416.4 l 181.2 416.3 l 181.5 416.3 l 181.8 416.2 l 182.1 416.2 l 182.4 416.3 l 182.7 416.4 l 183 416.5 l 183.3 416.7 l 183.6 416.9 l 183.9 417.2 l 184.2 417.5 l 184.5 417.9 l 184.8 418.3 l 185.1 418.8 l 185.5 419.4 l 185.8 420 l 186.1 420.7 l 186.4 421.4 l 186.7 422.2 l 187 423.1 l 187.3 424.1 l 187.6 425.1 l 187.9 426.1 l 188.2 427.3 l 188.5 428.5 l 188.8 429.8 l 189.1 431.1 l 189.4 432.5 l 189.7 434 l 190 435.5 l 190.4 437.1 l 190.7 438.8 l 191 440.5 l 191.3 442.3 l 191.6 444.2 l 191.9 446.1 l 192.2 448 l s n 192.2 448 m 192.5 450 l 192.8 452.1 l 193.1 454.2 l 193.4 456.3 l 193.7 458.5 l 194 460.7 l 194.3 463 l 194.6 465.2 l 194.9 467.5 l 195.3 469.9 l 195.6 472.2 l 195.9 474.6 l 196.2 477 l 196.5 479.3 l 196.8 481.7 l 197.1 484.1 l 197.4 486.5 l 197.7 488.9 l 198 491.3 l 198.3 493.7 l 198.6 496 l 198.9 498.4 l 199.2 500.7 l 199.5 503 l 199.8 505.2 l 200.2 507.4 l 200.5 509.6 l 200.8 511.8 l 201.1 513.9 l 201.4 516 l 201.7 518 l 202 520 l 202.3 522 l 202.6 523.9 l 202.9 525.7 l 203.2 527.5 l 203.5 529.2 l 203.8 530.9 l 204.1 532.5 l 204.4 534 l 204.7 535.5 l 205.1 536.9 l 205.4 538.3 l 205.7 539.6 l 206 540.8 l 206.3 541.9 l 206.6 543 l 206.9 544.1 l 207.2 545 l 207.5 545.9 l s n 207.5 545.9 m 207.8 546.7 l 208.1 547.5 l 208.4 548.2 l 208.7 548.8 l 209 549.3 l 209.3 549.8 l 209.6 550.3 l 210 550.6 l 210.3 550.9 l 210.6 551.1 l 210.9 551.3 l 211.2 551.4 l 211.5 551.4 l 211.8 551.4 l 212.1 551.3 l 212.4 551.2 l 212.7 551 l 213 550.8 l 213.3 550.5 l 213.6 550.1 l 213.9 549.7 l 214.2 549.3 l 214.5 548.8 l 214.9 548.2 l 215.2 547.6 l 215.5 547 l 215.8 546.3 l 216.1 545.5 l 216.4 544.8 l 216.7 543.9 l 217 543.1 l 217.3 542.2 l 217.6 541.3 l 217.9 540.3 l 218.2 539.3 l 218.5 538.3 l 218.8 537.3 l 219.1 536.2 l 219.4 535.1 l 219.8 533.9 l 220.1 532.8 l 220.4 531.6 l 220.7 530.4 l 221 529.2 l 221.3 527.9 l 221.6 526.7 l 221.9 525.4 l 222.2 524.1 l 222.5 522.8 l 222.8 521.5 l s n 222.8 521.5 m 223.1 520.1 l 223.4 518.8 l 223.7 517.4 l 224 516 l 224.3 514.7 l 224.7 513.3 l 225 511.9 l 225.3 510.5 l 225.6 509.1 l 225.9 507.7 l 226.2 506.3 l 226.5 504.8 l 226.8 503.4 l 227.1 502 l 227.4 500.6 l 227.7 499.2 l 228 497.7 l 228.3 496.3 l 228.6 494.9 l 228.9 493.5 l 229.2 492.1 l 229.6 490.7 l 229.9 489.3 l 230.2 487.9 l 230.5 486.5 l 230.8 485.1 l 231.1 483.8 l 231.4 482.4 l 231.7 481 l 232 479.7 l 232.3 478.3 l 232.6 477 l 232.9 475.7 l 233.2 474.4 l 233.5 473.1 l 233.8 471.8 l 234.1 470.5 l 234.5 469.2 l 234.8 468 l 235.1 466.7 l 235.4 465.5 l 235.7 464.3 l 236 463.1 l 236.3 462 l 236.6 460.8 l 236.9 459.7 l 237.2 458.6 l 237.5 457.5 l 237.8 456.4 l 238.1 455.4 l s n 238.1 455.4 m 238.4 454.4 l 238.7 453.4 l 239 452.5 l 239.4 451.6 l 239.7 450.7 l 240 449.9 l 240.3 449.1 l 240.6 448.4 l 240.9 447.7 l 241.2 447 l 241.5 446.4 l 241.8 445.9 l 242.1 445.4 l 242.4 445 l 242.7 444.6 l 243 444.3 l 243.3 444.1 l 243.6 444 l 243.9 443.9 l 244.3 443.9 l 244.6 444 l 244.9 444.2 l 245.2 444.4 l 245.5 444.8 l 245.8 445.2 l 246.1 445.8 l 246.4 446.4 l 246.7 447.1 l 247 448 l 247.3 448.9 l 247.6 449.9 l 247.9 451.1 l 248.2 452.3 l 248.5 453.6 l 248.8 455.1 l 249.2 456.6 l 249.5 458.3 l 249.8 460 l 250.1 461.9 l 250.4 463.8 l 250.7 465.9 l 251 468 l 251.3 470.3 l 251.6 472.6 l 251.9 475 l 252.2 477.5 l 252.5 480.1 l 252.8 482.7 l 253.1 485.5 l 253.4 488.3 l s n 253.4 488.3 m 253.7 491.1 l 254.1 494.1 l 254.4 497 l 254.7 500.1 l 255 503.1 l 255.3 506.3 l 255.6 509.4 l 255.9 512.6 l 256.2 515.8 l 256.5 519 l 256.8 522.3 l 257.1 525.5 l 257.4 528.8 l 257.7 532 l 258 535.3 l 258.3 538.5 l 258.6 541.7 l 259 544.9 l 259.3 548.1 l 259.6 551.2 l 259.9 554.3 l 260.2 557.3 l 260.5 560.3 l 260.8 563.3 l 261.1 566.2 l 261.4 569 l 261.7 571.8 l 262 574.5 l 262.3 577.2 l 262.6 579.7 l 262.9 582.2 l 263.2 584.6 l 263.5 587 l 263.9 589.2 l 264.2 591.4 l 264.5 593.5 l 264.8 595.4 l 265.1 597.3 l 265.4 599.1 l 265.7 600.8 l 266 602.4 l 266.3 604 l 266.6 605.4 l 266.9 606.7 l 267.2 607.9 l 267.5 609 l 267.8 610.1 l 268.1 611 l 268.4 611.8 l 268.8 612.6 l s n 268.8 612.6 m 269.1 613.2 l 269.4 613.8 l 269.7 614.2 l 270 614.6 l 270.3 614.8 l 270.6 615 l 270.9 615.1 l 271.2 615.1 l 271.5 615 l 271.8 614.8 l 272.1 614.6 l 272.4 614.2 l 272.7 613.8 l 273 613.3 l 273.3 612.7 l 273.7 612.1 l 274 611.3 l 274.3 610.5 l 274.6 609.7 l 274.9 608.7 l 275.2 607.7 l 275.5 606.7 l 275.8 605.6 l 276.1 604.4 l 276.4 603.2 l 276.7 601.9 l 277 600.5 l 277.3 599.2 l 277.6 597.7 l 277.9 596.2 l 278.2 594.7 l 278.6 593.2 l 278.9 591.6 l 279.2 589.9 l 279.5 588.2 l 279.8 586.5 l 280.1 584.8 l 280.4 583 l 280.7 581.2 l 281 579.4 l 281.3 577.5 l 281.6 575.7 l 281.9 573.8 l 282.2 571.9 l 282.5 569.9 l 282.8 568 l 283.1 566 l 283.5 564.1 l 283.8 562.1 l 284.1 560.1 l s n 284.1 560.1 m 284.4 558.1 l 284.7 556.1 l 285 554.1 l 285.3 552 l 285.6 550 l 285.9 548 l 286.2 546 l 286.5 543.9 l 286.8 541.9 l 287.1 539.9 l 287.4 537.9 l 287.7 535.9 l 288 533.8 l 288.4 531.8 l 288.7 529.8 l 289 527.8 l 289.3 525.9 l 289.6 523.9 l 289.9 521.9 l 290.2 520 l 290.5 518 l 290.8 516.1 l 291.1 514.2 l 291.4 512.3 l 291.7 510.4 l 292 508.5 l 292.3 506.6 l 292.6 504.8 l 292.9 502.9 l 293.3 501.1 l 293.6 499.3 l 293.9 497.5 l 294.2 495.8 l 294.5 494 l 294.8 492.3 l 295.1 490.6 l 295.4 488.9 l 295.7 487.2 l 296 485.6 l 296.3 483.9 l 296.6 482.3 l 296.9 480.8 l 297.2 479.2 l 297.5 477.7 l 297.8 476.2 l 298.2 474.7 l 298.5 473.3 l 298.8 471.9 l 299.1 470.5 l 299.4 469.2 l s n 299.4 469.2 m 299.7 467.9 l 300 466.6 l 300.3 465.4 l 300.6 464.2 l 300.9 463.1 l 301.2 462 l 301.5 461 l 301.8 460 l 302.1 459.1 l 302.4 458.3 l 302.7 457.5 l 303.1 456.7 l 303.4 456.1 l 303.7 455.5 l 304 455 l 304.3 454.6 l 304.6 454.2 l 304.9 454 l 305.2 453.8 l 305.5 453.7 l 305.8 453.8 l 306.1 453.9 l 306.4 454.1 l 306.7 454.4 l 307 454.8 l 307.3 455.4 l 307.6 456 l 308 456.7 l 308.3 457.6 l 308.6 458.6 l 308.9 459.7 l 309.2 460.9 l 309.5 462.2 l 309.8 463.6 l 310.1 465.2 l 310.4 466.8 l 310.7 468.6 l 311 470.5 l 311.3 472.5 l 311.6 474.6 l 311.9 476.8 l 312.2 479.1 l 312.5 481.5 l 312.9 484 l 313.2 486.6 l 313.5 489.3 l 313.8 492.1 l 314.1 495 l 314.4 497.9 l 314.7 500.9 l s n 314.7 500.9 m 315 504 l 315.3 507.1 l 315.6 510.3 l 315.9 513.6 l 316.2 516.9 l 316.5 520.2 l 316.8 523.5 l 317.1 526.9 l 317.4 530.3 l 317.8 533.8 l 318.1 537.2 l 318.4 540.6 l 318.7 544.1 l 319 547.5 l 319.3 550.9 l 319.6 554.3 l 319.9 557.7 l 320.2 561 l 320.5 564.3 l 320.8 567.6 l 321.1 570.8 l 321.4 574 l 321.7 577.1 l 322 580.2 l 322.3 583.1 l 322.7 586.1 l 323 588.9 l 323.3 591.7 l 323.6 594.4 l 323.9 597 l 324.2 599.5 l 324.5 601.9 l 324.8 604.3 l 325.1 606.5 l 325.4 608.7 l 325.7 610.7 l 326 612.7 l 326.3 614.5 l 326.6 616.2 l 326.9 617.9 l 327.2 619.4 l 327.6 620.9 l 327.9 622.2 l 328.2 623.4 l 328.5 624.5 l 328.8 625.5 l 329.1 626.5 l 329.4 627.3 l 329.7 628 l 330 628.5 l s n 330 628.5 m 330.3 629 l 330.6 629.4 l 330.9 629.7 l 331.2 629.9 l 331.5 630 l 331.8 630 l 332.1 629.9 l 332.5 629.7 l 332.8 629.4 l 333.1 629.1 l 333.4 628.6 l 333.7 628 l 334 627.4 l 334.3 626.7 l 334.6 625.9 l 334.9 625.1 l 335.2 624.1 l 335.5 623.1 l 335.8 622 l 336.1 620.9 l 336.4 619.7 l 336.7 618.4 l 337 617 l 337.4 615.6 l 337.7 614.2 l 338 612.7 l 338.3 611.1 l 338.6 609.5 l 338.9 607.9 l 339.2 606.2 l 339.5 604.4 l 339.8 602.6 l 340.1 600.8 l 340.4 599 l 340.7 597.1 l 341 595.2 l 341.3 593.2 l 341.6 591.2 l 341.9 589.2 l 342.3 587.2 l 342.6 585.1 l 342.9 583.1 l 343.2 581 l 343.5 578.9 l 343.8 576.8 l 344.1 574.6 l 344.4 572.5 l 344.7 570.3 l 345 568.2 l 345.3 566 l s n 345.3 566 m 345.6 563.8 l 345.9 561.6 l 346.2 559.4 l 346.5 557.2 l 346.8 555.1 l 347.2 552.9 l 347.5 550.7 l 347.8 548.5 l 348.1 546.3 l 348.4 544.2 l 348.7 542 l 349 539.8 l 349.3 537.7 l 349.6 535.5 l 349.9 533.4 l 350.2 531.3 l 350.5 529.2 l 350.8 527.1 l 351.1 525 l 351.4 522.9 l 351.7 520.8 l 352.1 518.8 l 352.4 516.8 l 352.7 514.7 l 353 512.7 l 353.3 510.8 l 353.6 508.8 l 353.9 506.8 l 354.2 504.9 l 354.5 503 l 354.8 501.1 l 355.1 499.2 l 355.4 497.4 l 355.7 495.5 l 356 493.7 l 356.3 491.9 l 356.6 490.2 l 357 488.4 l 357.3 486.7 l 357.6 485 l 357.9 483.4 l 358.2 481.7 l 358.5 480.1 l 358.8 478.5 l 359.1 476.9 l 359.4 475.4 l 359.7 473.9 l 360 472.5 l 360.3 471 l 360.6 469.7 l s n 360.6 469.7 m 360.9 468.3 l 361.2 467 l 361.5 465.7 l 361.9 464.5 l 362.2 463.4 l 362.5 462.2 l 362.8 461.2 l 363.1 460.2 l 363.4 459.2 l 363.7 458.3 l 364 457.5 l 364.3 456.8 l 364.6 456.1 l 364.9 455.5 l 365.2 454.9 l 365.5 454.5 l 365.8 454.1 l 366.1 453.8 l 366.4 453.6 l 366.8 453.5 l 367.1 453.5 l 367.4 453.6 l 367.7 453.7 l 368 454 l 368.3 454.4 l 368.6 454.9 l 368.9 455.5 l 369.2 456.2 l 369.5 457.1 l 369.8 458 l 370.1 459 l 370.4 460.2 l 370.7 461.5 l 371 462.9 l 371.3 464.4 l 371.7 466 l 372 467.7 l 372.3 469.5 l 372.6 471.5 l 372.9 473.5 l 373.2 475.7 l 373.5 477.9 l 373.8 480.3 l 374.1 482.7 l 374.4 485.2 l 374.7 487.9 l 375 490.6 l 375.3 493.3 l 375.6 496.2 l 375.9 499.1 l s n 375.9 499.1 m 376.2 502.1 l 376.6 505.1 l 376.9 508.2 l 377.2 511.4 l 377.5 514.6 l 377.8 517.8 l 378.1 521 l 378.4 524.3 l 378.7 527.6 l 379 530.9 l 379.3 534.2 l 379.6 537.6 l 379.9 540.9 l 380.2 544.2 l 380.5 547.5 l 380.8 550.8 l 381.1 554 l 381.5 557.2 l 381.8 560.4 l 382.1 563.5 l 382.4 566.6 l 382.7 569.6 l 383 572.6 l 383.3 575.5 l 383.6 578.4 l 383.9 581.2 l 384.2 583.9 l 384.5 586.5 l 384.8 589.1 l 385.1 591.6 l 385.4 593.9 l 385.7 596.2 l 386 598.5 l 386.4 600.6 l 386.7 602.6 l 387 604.5 l 387.3 606.4 l 387.6 608.1 l 387.9 609.7 l 388.2 611.3 l 388.5 612.7 l 388.8 614 l 389.1 615.2 l 389.4 616.3 l 389.7 617.4 l 390 618.3 l 390.3 619.1 l 390.6 619.8 l 390.9 620.4 l 391.3 620.9 l s n 391.3 620.9 m 391.6 621.3 l 391.9 621.6 l 392.2 621.8 l 392.5 622 l 392.8 622 l 393.1 621.9 l 393.4 621.7 l 393.7 621.5 l 394 621.2 l 394.3 620.7 l 394.6 620.2 l 394.9 619.6 l 395.2 619 l 395.5 618.2 l 395.8 617.4 l 396.2 616.5 l 396.5 615.5 l 396.8 614.5 l 397.1 613.4 l 397.4 612.2 l 397.7 611 l 398 609.7 l 398.3 608.3 l 398.6 606.9 l 398.9 605.5 l 399.2 604 l 399.5 602.4 l 399.8 600.8 l 400.1 599.2 l 400.4 597.5 l 400.7 595.8 l 401.1 594 l 401.4 592.2 l 401.7 590.4 l 402 588.5 l 402.3 586.6 l 402.6 584.7 l 402.9 582.7 l 403.2 580.8 l 403.5 578.8 l 403.8 576.8 l 404.1 574.7 l 404.4 572.7 l 404.7 570.6 l 405 568.5 l 405.3 566.5 l 405.6 564.4 l 406 562.2 l 406.3 560.1 l 406.6 558 l s n 406.6 558 m 406.9 555.9 l 407.2 553.8 l 407.5 551.6 l 407.8 549.5 l 408.1 547.4 l 408.4 545.3 l 408.7 543.1 l 409 541 l 409.3 538.9 l 409.6 536.8 l 409.9 534.7 l 410.2 532.6 l 410.5 530.5 l 410.9 528.4 l 411.2 526.4 l 411.5 524.3 l 411.8 522.3 l 412.1 520.2 l 412.4 518.2 l 412.7 516.2 l 413 514.2 l 413.3 512.2 l 413.6 510.3 l 413.9 508.3 l 414.2 506.4 l 414.5 504.5 l 414.8 502.6 l 415.1 500.7 l 415.4 498.9 l 415.8 497 l 416.1 495.2 l 416.4 493.4 l 416.7 491.6 l 417 489.8 l 417.3 488.1 l 417.6 486.4 l 417.9 484.7 l 418.2 483 l 418.5 481.4 l 418.8 479.7 l 419.1 478.1 l 419.4 476.5 l 419.7 475 l 420 473.5 l 420.3 472 l 420.7 470.5 l 421 469.1 l 421.3 467.7 l 421.6 466.3 l 421.9 465 l s n 421.9 465 m 422.2 463.7 l 422.5 462.4 l 422.8 461.2 l 423.1 460.1 l 423.4 459 l 423.7 457.9 l 424 456.9 l 424.3 455.9 l 424.6 455 l 424.9 454.1 l 425.2 453.3 l 425.6 452.6 l 425.9 451.9 l 426.2 451.4 l 426.5 450.8 l 426.8 450.4 l 427.1 450 l 427.4 449.7 l 427.7 449.5 l 428 449.4 l 428.3 449.4 l 428.6 449.5 l 428.9 449.6 l 429.2 449.9 l 429.5 450.3 l 429.8 450.7 l 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216.4 404.6 l 216.7 403.4 l 217 402.2 l 217.3 401.2 l 217.6 400.1 l 217.9 399.1 l 218.2 398.2 l 218.5 397.3 l 218.8 396.5 l 219.1 395.7 l 219.4 394.9 l 219.8 394.2 l 220.1 393.5 l 220.4 392.8 l 220.7 392.2 l 221 391.6 l 221.3 391 l 221.6 390.5 l 221.9 389.9 l 222.2 389.4 l 222.5 389 l 222.8 388.5 l s n 222.8 388.5 m 223.1 388.1 l 223.4 387.7 l 223.7 387.3 l 224 387 l 224.3 386.6 l 224.7 386.3 l 225 386 l 225.3 385.7 l 225.6 385.4 l 225.9 385.1 l 226.2 384.9 l 226.5 384.6 l 226.8 384.4 l 227.1 384.2 l 227.4 384 l 227.7 383.8 l 228 383.6 l 228.3 383.4 l 228.6 383.2 l 228.9 383.1 l 229.2 382.9 l 229.6 382.8 l 229.9 382.6 l 230.2 382.5 l 230.5 382.4 l 230.8 382.2 l 231.1 382.1 l 231.4 382 l 231.7 381.9 l 232 381.8 l 232.3 381.7 l 232.6 381.6 l 232.9 381.6 l 233.2 381.5 l 233.5 381.4 l 233.8 381.3 l 234.1 381.3 l 234.5 381.2 l 234.8 381.1 l 235.1 381.1 l 235.4 381 l 235.7 381 l 236 380.9 l 236.3 380.9 l 236.6 380.8 l 236.9 380.8 l 237.2 380.8 l 237.5 380.7 l 237.8 380.7 l 238.1 380.6 l s n 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546.4 l 260.2 543.6 l 260.5 540.7 l 260.8 537.5 l 261.1 534.1 l 261.4 530.6 l 261.7 526.9 l 262 523.2 l 262.3 519.3 l 262.6 515.4 l 262.9 511.5 l 263.2 507.5 l 263.5 503.5 l 263.9 499.5 l 264.2 495.5 l 264.5 491.6 l 264.8 487.7 l 265.1 483.8 l 265.4 480 l 265.7 476.3 l 266 472.7 l 266.3 469.1 l 266.6 465.6 l 266.9 462.2 l 267.2 458.9 l 267.5 455.6 l 267.8 452.5 l 268.1 449.5 l 268.4 446.5 l 268.8 443.7 l s n 268.8 443.7 m 269.1 440.9 l 269.4 438.3 l 269.7 435.7 l 270 433.2 l 270.3 430.8 l 270.6 428.6 l 270.9 426.4 l 271.2 424.2 l 271.5 422.2 l 271.8 420.3 l 272.1 418.4 l 272.4 416.6 l 272.7 414.9 l 273 413.2 l 273.3 411.7 l 273.7 410.2 l 274 408.7 l 274.3 407.3 l 274.6 406 l 274.9 404.8 l 275.2 403.6 l 275.5 402.4 l 275.8 401.3 l 276.1 400.3 l 276.4 399.3 l 276.7 398.4 l 277 397.5 l 277.3 396.6 l 277.6 395.8 l 277.9 395 l 278.2 394.3 l 278.6 393.5 l 278.9 392.9 l 279.2 392.2 l 279.5 391.6 l 279.8 391 l 280.1 390.5 l 280.4 390 l 280.7 389.5 l 281 389 l 281.3 388.5 l 281.6 388.1 l 281.9 387.7 l 282.2 387.3 l 282.5 386.9 l 282.8 386.6 l 283.1 386.3 l 283.5 385.9 l 283.8 385.6 l 284.1 385.4 l s n 284.1 385.4 m 284.4 385.1 l 284.7 384.8 l 285 384.6 l 285.3 384.3 l 285.6 384.1 l 285.9 383.9 l 286.2 383.7 l 286.5 383.5 l 286.8 383.3 l 287.1 383.2 l 287.4 383 l 287.7 382.9 l 288 382.7 l 288.4 382.6 l 288.7 382.4 l 289 382.3 l 289.3 382.2 l 289.6 382.1 l 289.9 382 l 290.2 381.9 l 290.5 381.8 l 290.8 381.7 l 291.1 381.6 l 291.4 381.5 l 291.7 381.4 l 292 381.4 l 292.3 381.3 l 292.6 381.2 l 292.9 381.2 l 293.3 381.1 l 293.6 381.1 l 293.9 381 l 294.2 380.9 l 294.5 380.9 l 294.8 380.9 l 295.1 380.8 l 295.4 380.8 l 295.7 380.7 l 296 380.7 l 296.3 380.7 l 296.6 380.6 l 296.9 380.6 l 297.2 380.6 l 297.5 380.5 l 297.8 380.5 l 298.2 380.5 l 298.5 380.5 l 298.8 380.4 l 299.1 380.4 l 299.4 380.4 l s n 299.4 380.4 m 299.7 380.4 l 300 380.3 l 300.3 380.3 l 300.6 380.3 l 300.9 380.3 l 301.2 380.3 l 301.5 380.3 l 301.8 380.3 l 302.1 380.2 l 302.4 380.2 l 302.7 380.2 l 303.1 380.2 l 303.4 380.2 l 303.7 380.2 l 304 380.2 l 304.3 380.2 l 304.6 380.2 l 304.9 380.2 l 305.2 380.3 l 305.5 380.4 l 305.8 380.5 l 306.1 380.6 l 306.4 380.9 l 306.7 381.2 l 307 381.6 l 307.3 382.1 l 307.6 382.8 l 308 383.6 l 308.3 384.6 l 308.6 385.8 l 308.9 387.3 l 309.2 389 l 309.5 390.9 l 309.8 393.1 l 310.1 395.6 l 310.4 398.4 l 310.7 401.4 l 311 404.7 l 311.3 408.3 l 311.6 412 l 311.9 415.9 l 312.2 420 l 312.5 424.2 l 312.9 428.5 l 313.2 432.8 l 313.5 437.2 l 313.8 441.4 l 314.1 445.6 l 314.4 449.7 l 314.7 453.6 l s n 314.7 453.6 m 315 457.4 l 315.3 460.9 l 315.6 464.2 l 315.9 467.2 l 316.2 469.9 l 316.5 472.4 l 316.8 474.5 l 317.1 476.3 l 317.4 477.9 l 317.8 479.1 l 318.1 480 l 318.4 480.6 l 318.7 480.9 l 319 481 l 319.3 480.8 l 319.6 480.3 l 319.9 479.6 l 320.2 478.7 l 320.5 477.6 l 320.8 476.3 l 321.1 474.8 l 321.4 473.2 l 321.7 471.4 l 322 469.6 l 322.3 467.6 l 322.7 465.6 l 323 463.4 l 323.3 461.3 l 323.6 459 l 323.9 456.8 l 324.2 454.5 l 324.5 452.2 l 324.8 449.9 l 325.1 447.6 l 325.4 445.3 l 325.7 443.1 l 326 440.8 l 326.3 438.6 l 326.6 436.4 l 326.9 434.3 l 327.2 432.2 l 327.6 430.2 l 327.9 428.2 l 328.2 426.2 l 328.5 424.4 l 328.8 422.5 l 329.1 420.7 l 329.4 419 l 329.7 417.3 l 330 415.7 l s n 330 415.7 m 330.3 414.2 l 330.6 412.7 l 330.9 411.2 l 331.2 409.8 l 331.5 408.5 l 331.8 407.2 l 332.1 405.9 l 332.5 404.7 l 332.8 403.6 l 333.1 402.5 l 333.4 401.4 l 333.7 400.4 l 334 399.5 l 334.3 398.5 l 334.6 397.6 l 334.9 396.8 l 335.2 396 l 335.5 395.2 l 335.8 394.5 l 336.1 393.8 l 336.4 393.1 l 336.7 392.5 l 337 391.8 l 337.4 391.3 l 337.7 390.7 l 338 390.2 l 338.3 389.7 l 338.6 389.2 l 338.9 388.7 l 339.2 388.3 l 339.5 387.9 l 339.8 387.5 l 340.1 387.1 l 340.4 386.8 l 340.7 386.4 l 341 386.1 l 341.3 385.8 l 341.6 385.5 l 341.9 385.2 l 342.3 385 l 342.6 384.7 l 342.9 384.5 l 343.2 384.2 l 343.5 384 l 343.8 383.8 l 344.1 383.6 l 344.4 383.4 l 344.7 383.3 l 345 383.1 l 345.3 382.9 l s n 345.3 382.9 m 345.6 382.8 l 345.9 382.6 l 346.2 382.5 l 346.5 382.4 l 346.8 382.3 l 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Fi(g)23 b Fv(=)f Fk(n)p Fv(!)14 b Fk(T)1411 3993 y Fw(K)1466 3981 y Fv(\()p Fk(\033)s Fv(\))1580 3947 y Fj(n)1626 3914 y Fh(\002)1660 3981 y Fv(1)k(+)g Fi(O)r Fv(\()p Fk(T)9 b(=T)2052 3993 y Fw(K)2107 3981 y Fv(\()p Fk(\033)s Fv(\)\))19 b(+)g Fi(O)r Fv(\()p Fk(r)r Fv(\()p Fk(\033)s Fv(\)\))2641 3914 y Fh(\003)2678 3981 y Fk(;)655 b Fv(\(18\))133 4133 y(indep)r(enden)n(tly)22 b(of)g(the)g(v)-5 b(alue)21 b(of)h Fk(\025T)12 b Fv(.)34 b(This)21 b(is)h(due)g(to)f(the)h(fact)g(that)g(the)f(p)r(erio)r(d)h (of)f(mo)r(dulation)h(is)f(short)133 4233 y(with)h(resp)r(ect)f(to)h (the)g(scale)f(of)h(exp)r(onen)n(tial)f(deca)n(y)-7 b(.)34 b(The)21 b(momen)n(ts)h(of)f(the)h(residence-time)g(distribution)133 4333 y(can)27 b(th)n(us)h(di\013er)g(signi\014can)n(tly)f(from)g(those) h(of)f(an)h(exp)r(onen)n(tial)f(distribution)h(only)g(when)g Fk(T)38 b Fv(is)28 b(not)g(to)r(o)133 4432 y(small)f(compared)g(to)g(b) r(oth)h Fk(\025)1074 4402 y Fu(\000)p Fw(1)1191 4432 y Fv(and)g Fk(T)1402 4444 y Fw(K)1456 4432 y Fv(\()p Fk(\033)s Fv(\).)257 4533 y(A)e(third)f(limit)h(in)f(whic)n(h)g(the)g (residence-time)g(distribution)g(should)g(approac)n(h)e(an)h(exp)r (onen)n(tial)h(one)133 4633 y(is)35 b(the)h(limit)g(of)f(v)-5 b(anishing)35 b(forcing)g(amplitude)g Fk(A)h Fv(\(for)f(the)h (particular)e(case)h(of)g(the)h(p)r(oten)n(tial)f(\(2\)\).)133 4732 y(Ho)n(w)n(ev)n(er,)j(the)f(expression)f(\(6\))h(do)r(es)g(not)g (hold)h(in)f(cases)f(where)h Fk(A)g Fv(is)h(not)f(large)f(compared)g (to)h Fk(\033)3443 4702 y Fw(2)3480 4732 y Fv(,)133 4832 y(b)r(ecause)31 b(it)i(mak)n(es)e(use)h(of)g(the)g(saddle-p)r(oin)n(t)g (metho)r(d)g(in)h(the)f(vicinit)n(y)g(of)g(MPEPs.)49 b(An)32 b(asymptotic)133 4932 y(expression)26 b(for)h Fk(A)c Fi(\034)g Fk(\033)901 4901 y Fw(2)967 4932 y Fv(has)k(b)r(een)h (prop)r(osed)e(in)i([13,)11 b(14].)p eop %%Page: 7 7 7 6 bop 166 -141 a Fg(N.)28 b(Ber)n(glund)d Fs(and)j Fg(B.)f(Gentz)p Fv(:)g Fx(Residence)33 b(times)e(f)n(or)h(stochastic)g (resonance)473 b Fl(7)291 149 y Ft(Conclusion.)49 b({)85 b Fv(The)31 b(most)g(imp)r(ortan)n(t)g(asp)r(ect)g(of)g(our)f(rigorous) e(expression)i(for)g(the)i(residence-)166 249 y(time)f(distribution)f (is)f(the)i(fact)f(that)g(it)h(is)e(go)n(v)n(erned)f(essen)n(tially)h (b)n(y)h(t)n(w)n(o)f(dimensionless)g(parameters,)166 349 y Fk(\025T)42 b Fv(and)29 b Fk(T)9 b(=T)617 361 y Fw(K)671 349 y Fv(\()p Fk(\033)s Fv(\),)32 b(whic)n(h)e(can)f(b)r(e)i (mo)r(di\014ed)f(indep)r(enden)n(tly)-7 b(.)45 b(The)30 b(ratio)f Fk(T)9 b(=T)2784 361 y Fw(K)2838 349 y Fv(\()p Fk(\033)s Fv(\))31 b(b)r(et)n(w)n(een)f(p)r(erio)r(d)166 448 y(and)i(Kramers)e(time)i(app)r(ears)f(in)h(most)g(quan)n(titativ)n (e)f(measures)g(of)h(SR,)g(whic)n(h)g(indicate)g(an)g(optimal)166 548 y(ampli\014cation)j(when)g Fk(T)46 b Fv(is)35 b(close)f(to)h(2)p Fk(T)1488 560 y Fw(K)1542 548 y Fv(\()p Fk(\033)s Fv(\).)60 b(In)36 b(this)f(regime,)h(the)g(probabilit)n(y)e(of)h(transitions)f(b) r(e-)166 648 y(t)n(w)n(een)24 b(p)r(oten)n(tial)f(w)n(ells)h(b)r 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b(resonance.)51 b Fp(R)l(ep)l(orts)35 b(on)d(Pr)l(o)l(gr)l(ess)j(in)352 3470 y(Physics)p Fs(,)27 b(67:45{105,)i(2004.)204 3562 y([8])68 b(Mark)32 b(I.)g(F)-6 b(reidlin.)53 b(Quasi-deterministic)32 b(appro)n(ximation,)h(metastabilit)n(y)f(and)f(sto)r(c)n(hastic)j (resonance.)352 3653 y Fp(Physic)l(a)28 b(D)p Fs(,)e(137:333{352,)k (2000.)204 3744 y([9])68 b(P)-6 b(.)39 b(Imk)n(eller)g(and)g(I.)g(P)n (a)n(vlyuk)n(evic)n(h.)73 b(Mo)r(del)40 b(reduction)g(and)e(sto)r(c)n (hastic)j(resonance.)76 b Fp(Sto)l(ch.)41 b(Dyn.)p Fs(,)352 3836 y(2\(4\):463{506,)29 b(2002.)166 3927 y([10])68 b(Nils)26 b(Berglund)f(and)g(Barbara)i(Gen)n(tz.)34 b(A)24 b(sample-paths)h(approac)n(h)h(to)f(noise-induced)g(sync)n (hronization:)352 4018 y(Sto)r(c)n(hastic)h(resonance)h(in)e(a)h (double-w)n(ell)h(p)r(oten)n(tial.)35 b Fp(A)n(nn.)27 b(Appl.)g(Pr)l(ob)l(ab.)p Fs(,)g(12:1419{1470,)j(2002.)166 4110 y([11])68 b(Nils)32 b(Berglund)f(and)g(Barbara)i(Gen)n(tz.)51 b(Bey)n(ond)31 b(the)g(F)-6 b(okk)n(er{Planc)n(k)31 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606 y(Pr)l(ob)l(ab.)p Fs(,)27 b(20\(3\):1385{1419,)j(1992.)133 697 y([19])68 b(Martin)29 b(V.)f(Da)n(y)-6 b(.)43 b(Cycling)29 b(and)f(sk)n(ewing)i(of)f(exit)f (measures)h(for)g(planar)g(systems.)43 b Fp(Sto)l(ch.)31 b(Sto)l(ch.)g(R)l(ep.)p Fs(,)319 789 y(48:227{247,)f(1994.)133 880 y([20])68 b(Rob)r(ert)22 b(S.)h(Maier)g(and)g(D.)f(L.)h(Stein.)29 b(Oscillatory)24 b(b)r(eha)n(vior)f(of)g(the)g(rate)g(of)g(escap)r(e)h (through)e(an)g(unstable)319 971 y(limit)j(cycle.)35 b Fp(Phys.)28 b(R)l(ev.)f(L)l(ett.)p Fs(,)g(77\(24\):4860{4863,)k (1996.)133 1063 y([21])68 b(J\177)-38 b(org)37 b(Lehmann,)f(P)n(eter)g (Reimann,)i(and)d(P)n(eter)h(H\177)-38 b(anggi.)65 b(Surmoun)n(ting)33 b(oscillating)38 b(barriers:)56 b(Path-)319 1154 y(in)n(tegral)26 b(approac)n(h)g(for)h(w)n(eak)f(noise.)35 b Fp(Phys.)28 b(R)l(ev.)f(E)p Fs(,)f(62\(5\):6282{6303,)31 b(2000.)133 1245 y([22])68 b(M.)29 b(I.)h(Dykman,)e(B.)h(Golding,)j(L.)d(I.)g (McCann,)i(V.)e(N.)g(Smely)n(anskiy)-6 b(,)28 b(D.)h(G.)h(Luc)n(hinsky) -6 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