Existence and convergence results for infinite dimensional nonlinear stochastic equations with multiplicative noise

Viorel Barbu, Zdzisław Brzeźniak, Erika Hausenblas and Luciano Tubaro

Stochastic Processes and their Applications, 2013, vol. 123, issue 3, 934-951

Abstract: The solution Xn to a nonlinear stochastic differential equation of the form dXn(t)+An(t)Xn(t)dt−12∑j=1N(Bjn(t))2Xn(t)dt=∑j=1NBjn(t)Xn(t)dβjn(t)+fn(t)dt, Xn(0)=x, where βjn is a regular approximation of a Brownian motion βj, Bjn(t) is a family of linear continuous operators from V to H strongly convergent to Bj(t), An(t)→A(t), {An(t)} is a family of maximal monotone nonlinear operators of subgradient type from V to V′, is convergent to the solution to the stochastic differential equation dX(t)+A(t)X(t)dt−12∑j=1NBj2(t)X(t)dt=∑j=1NBj(t)X(t)dβj(t)+f(t)dt, X(0)=x. Here V⊂H≅H′⊂V′ where V is a reflexive Banach space with dual V′ and H is a Hilbert space. These results can be reformulated in terms of Stratonovich stochastic equation dY(t)+A(t)Y(t)dt=∑j=1NBj(t)Y(t)∘dβj(t)+f(t)dt.

Keywords: Stochastic differential equations; Brownian motion; Progressively measurable; Porous media equations (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2012.10.008

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