TY - CHAP

T1 - Noise-Induced Escape From an Attractor

AU - Schuss, Zeev

N1 - Publisher Copyright:
© 2010, Springer Science+Business Media, LLC.

PY - 2010

Y1 - 2010

N2 - The analysis of the exit problem, as defined in Section 6.4 and analyzed in Chapter 6, was based on explicit integral representations of solutions to the one-dimensional Andronov–Vitt–Pontryagin boundary value problems (6.33) for the exit distribution and for the MFPT. Such representations are in general unavailable in higher dimensions so that there is no obvious generalization of these methods for the exit problem in higher dimensions. Another approach, that is based on constructing an asymptotic solution to the boundary value problems by the methods of singular perturbations, can be generalized to higher dimensions (see Section 10.2).

AB - The analysis of the exit problem, as defined in Section 6.4 and analyzed in Chapter 6, was based on explicit integral representations of solutions to the one-dimensional Andronov–Vitt–Pontryagin boundary value problems (6.33) for the exit distribution and for the MFPT. Such representations are in general unavailable in higher dimensions so that there is no obvious generalization of these methods for the exit problem in higher dimensions. Another approach, that is based on constructing an asymptotic solution to the boundary value problems by the methods of singular perturbations, can be generalized to higher dimensions (see Section 10.2).

KW - Boundary Layer

KW - Boundary Layer Equation

KW - Eikonal Equation

KW - Exit Point

KW - Saddle Point

UR - http://www.scopus.com/inward/record.url?scp=85067937530&partnerID=8YFLogxK

U2 - 10.1007/978-1-4419-1605-1_10

DO - 10.1007/978-1-4419-1605-1_10

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AN - SCOPUS:85067937530

T3 - Applied Mathematical Sciences (Switzerland)

SP - 339

EP - 398

BT - Applied Mathematical Sciences (Switzerland)

PB - Springer

ER -