Displaying similar documents to “Asymptotic Properties of Stochastic Semilinear Equations by the Method of Lower Measures”

Uniform exponential ergodicity of stochastic dissipative systems

Beniamin Goldys, Bohdan Maslowski (2001)

Czechoslovak Mathematical Journal

Similarity:

We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in ℝ d with d ≤ 3 .

Invariant measures for nonlinear SPDE's: uniqueness and stability

Bohdan Maslowski, Jan Seidler (1998)

Archivum Mathematicum

Similarity:

The paper presents a review of some recent results on uniqueness of invariant measures for stochastic differential equations in infinite-dimensional state spaces, with particular attention paid to stochastic partial differential equations. Related results on asymptotic behaviour of solutions like ergodic theorems and convergence of probability laws of solutions in strong and weak topologies are also reviewed.

Approximation of the Zakai equation in a nonlinear filtering problem with delay

Krystyna Twardowska, Tomasz Marnik, Monika Pasławska-Południak (2003)

International Journal of Applied Mathematics and Computer Science

Similarity:

A nonlinear filtering problem with delays in the state and observation equations is considered. The unnormalized conditional probability density of the filtered diffusion process satisfies the so-called Zakai equation and solves the nonlinear filtering problem. We examine the solution of the Zakai equation using an approximation result. Our theoretical deliberations are illustrated by a numerical example.