Abstract
AbstractThe random walk (approximating the Wiener process in the area of normal deviations) and the Wiener process have, in general, different asymptotics of the large deviation probabilities. Therefore, special arrangements in the numerical procedures should be made to calculate solutions of various problems related to the large deviations for the Wiener process and for the corresponding PDE’s with a small parameter. Exit problem, wavefront propagation, stochastic resonance are among these problems. We calculate the action functional when the Wiener process is replaced by the random walk, find the relation between the small parameters which provide convergence to the solution of the problem with the Gaussian white noise as the perturbation, and calculate the correction term.KeywordsStochastic resonancecomputer simulationnumerical methods for PDE’s with a small parameterlarge deviations
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