TY - JOUR

T1 - Some results on the problem of exit from a domain

AU - Bobrovsky, Ben Zion

AU - Zeitouni, Ofer

N1 - Funding Information:
Correspondence lo: Dr. 0. Zeitouni, Department of Electrical Engineering, Technion - Israel Institute of Technology, Technion City, Haifa 32000, Israel. * The work of this author was partially done while visiting the Laboratory for Information and Decision Systems at MIT, under support from an AFSOR grant 85-0227B, a US Army Research Office contract DAAL03-86-K-0171 and the Technion V.P.R. Coleman Cohen research fund.

PY - 1992/6

Y1 - 1992/6

N2 - The problem of exit from a domain of attraction of a stable equilibrium point in the presence of small noise is considered for a class of two-dimensional systems. It is shown that for these systems, the exit measure is 'skewed' in the sense that if S denotes the saddle point in the quasipotential towards which the exit measure collapses as the noise intensity goes to zero, then there exists an ε dependent neighborhood Δ of S such that lim P(exit in Δ)/{divides}Δ{divides}=0. Thus, the most probable exit point is not S but is rather skewed aside by εγ for some γ. The behaviour of such skewness, which was predicted by asymptotic expansions, depends on the ratio of normal to tangential forces around the saddle point.

AB - The problem of exit from a domain of attraction of a stable equilibrium point in the presence of small noise is considered for a class of two-dimensional systems. It is shown that for these systems, the exit measure is 'skewed' in the sense that if S denotes the saddle point in the quasipotential towards which the exit measure collapses as the noise intensity goes to zero, then there exists an ε dependent neighborhood Δ of S such that lim P(exit in Δ)/{divides}Δ{divides}=0. Thus, the most probable exit point is not S but is rather skewed aside by εγ for some γ. The behaviour of such skewness, which was predicted by asymptotic expansions, depends on the ratio of normal to tangential forces around the saddle point.

KW - asymptotic expansions

KW - characteristic boundary

KW - exit problem

KW - large deviations

KW - two-dimensional diffusions

UR - http://www.scopus.com/inward/record.url?scp=0011219712&partnerID=8YFLogxK

U2 - 10.1016/0304-4149(92)90124-9

DO - 10.1016/0304-4149(92)90124-9

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AN - SCOPUS:0011219712

SN - 0304-4149

VL - 41

SP - 241

EP - 256

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -