Wong-Zakai approximations of stochastic evolution equations View Full Text


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Article Info

DATE

2006-09-12

AUTHORS

Gianmario Tessitore, Jerzy Zabczyk

ABSTRACT

.Theorems on weak convergence of the laws of the Wong-Zakai approximations for evolution equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \begin{aligned} dX(t) & = (AX(t) + F(X(t)))dt + G(X(t))dW(t)\\ X(0) & = x \in H \end{aligned} $$\end{document} are proved. The operator A in the equation generates an analytic semigroup of linear operators on a Hilbert space H. The tightness of the approximating sequence is established using the stochastic factorisation formula. Applications to strongly damped wave and plate equations as well as to stochastic invariance are discussed. More... »

PAGES

621-655

References to SciGraph publications

  • 1994. A simple proof of the support theorem for diffusion processes in SÉMINAIRE DE PROBABILITÉS XXVIII
  • 1994-09. The support of the solution to a hyperbolic SPDE in PROBABILITY THEORY AND RELATED FIELDS
  • 1969. Riemann-Stieltjes approximations of stochastic integrals in PROBABILITY THEORY AND RELATED FIELDS
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    http://scigraph.springernature.com/pub.10.1007/s00028-006-0280-9

    DOI

    http://dx.doi.org/10.1007/s00028-006-0280-9

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