skip to main content

SciTech ConnectSciTech Connect

Title: On large deviations for ensembles of distributions

The paper is concerned with the large deviations problem in the Freidlin-Wentzell formulation without the assumption of the uniqueness of the solution to the equation involving white noise. In other words, it is assumed that for each ε>0 the nonempty set P{sub ε} of weak solutions is not necessarily a singleton. Analogues of a number of concepts in the theory of large deviations are introduced for the set (P{sub ε}, ε>0), hereafter referred to as an ensemble of distributions. The ensembles of weak solutions of an n-dimensional stochastic Navier-Stokes system and stochastic wave equation with power-law nonlinearity are shown to be uniformly exponentially tight. An idempotent Wiener process in a Hilbert space and idempotent partial differential equations are defined. The accumulation points in the sense of large deviations of the ensembles in question are shown to be weak solutions of the corresponding idempotent equations. Bibliography: 14 titles.
Authors:
 [1]
  1. Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University), Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22365877
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; HILBERT SPACE; MATHEMATICAL SOLUTIONS; NAVIER-STOKES EQUATIONS; NOISE; NONLINEAR PROBLEMS; STOCHASTIC PROCESSES; WAVE EQUATIONS