Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times

Journal Article · Mon May 01 00:00:00 EDT 1989 · Journal of Statistical Physics; (USA)

DOI:https://doi.org/10.1007/BF01041595· OSTI ID:5394601

Martinelli, F; Olivieri, E; Scoppola, E ^[1]

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1. Universita La Sapienza, Rome (Italy)

The authors apply previous results on the pathwise exponential loss of memory of the initial condition for stochastic differential equations with small diffusion to the problem of the asymptotic distribution of the first exit times from an attracted domain. They show under general hypotheses that the suitably rescaled exit time converges in the zero-noise limit to an exponential random variable. Then they extend the results to an infinite-dimensional case obtained by adding a small random perturbation to a nonlinear heat equation.

• OSTI ID: 5394601
• Journal Information: Journal of Statistical Physics; (USA), Vol. 55:3-4; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFUSION
PERTURBATION THEORY
STOCHASTIC PROCESSES
BROWNIAN MOVEMENT
CONVERGENCE
CRYSTAL MODELS
DIFFERENTIAL EQUATIONS
FERROMAGNETIC MATERIALS
FLUCTUATIONS
GAUSS FUNCTION
HARMONIC OSCILLATOR MODELS
HEAT TRANSFER
MANY-DIMENSIONAL CALCULATIONS
MARKOV PROCESS
NOISE
NONLINEAR PROBLEMS
RANDOMNESS
STATISTICAL MECHANICS
TIME DEPENDENCE
TRANSPORT THEORY
TUNNEL EFFECT
ENERGY TRANSFER
EQUATIONS
FUNCTIONS
MAGNETIC MATERIALS
MATERIALS
MATHEMATICAL MODELS
MECHANICS
VARIATIONS
656002* - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-)
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics