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Stability of Markov processes nonhomogeneous in time

Marta Tyran-Kamińska (1999)

Annales Polonici Mathematici

We study the asymptotic behaviour of discrete time processes which are products of time dependent transformations defined on a complete metric space. Our sufficient condition is applied to products of Markov operators corresponding to stochastically perturbed dynamical systems and fractals.

Stability of precise Laplace's method under approximations; Applications

A. Guionnet (2010)

ESAIM: Probability and Statistics

We study the fluctuations around non degenerate attractors of the empirical measure under mean field Gibbs measures. We prove that a mild change of the densities of these measures does not affect the central limit theorems. We apply this result to generalize the assumptions of [3] and [12] on the densities of the Gibbs measures to get precise Laplace estimates.

Stability of solutions of BSDEs with random terminal time

Sandrine Toldo (2006)

ESAIM: Probability and Statistics

In this paper, we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely finite random terminal time. More precisely, we are going to show that if (Wn) is a sequence of scaled random walks or a sequence of martingales that converges to a Brownian motion W and if ( τ n ) is a sequence of stopping times that converges to a stopping time τ, then the solution of the BSDE driven by Wn with random terminal time τ n converges to the solution...

Stability of stochastic optimization problems - nonmeasurable case

Petr Lachout (2008)

Kybernetika

This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, ε -optimal solutions are considered. The setup is illustrated on consistency of a ε - M -estimator in linear regression model.

Stability of stochastic processes defined by integral functionals

K. Urbanik (1992)

Studia Mathematica

The paper is devoted to the study of integral functionals ʃ 0 f ( X ( t , ω ) ) d t for continuous nonincreasing functions f and nonnegative stochastic processes X(t,ω) with stationary and independent increments. In particular, a concept of stability defined in terms of the functionals ʃ 0 f ( a X ( t , ω ) ) d t with a ∈ (0,∞) is discussed.

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