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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Barbu, Viorel^1,2  Brzezniak, Zdzislaw³  Hausenblas, Erika⁴  Tubaro, Luciano⁵ 

[1] Alexandru Ioan Cuza Univ, Iasi, Romania

[2] Inst Math Octav Mayer, Iasi, Romania

[3] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

[4] Univ Leoben, Dept Math & Informat Technol, A-8700 Leoben, Austria

[5] Univ Trento, Dept Math, Trento, Italy

关键词: Stochastic differential equations;    Brownian motion;    Progressively measurable;    Porous media equations;   

DOI  :  10.1016/j.spa.2012.10.008

来源: Elsevier

【 摘 要 】

The solution X-n to a nonlinear stochastic differential equation of the form d X-n(t) + A(n)(t) X-n(t) dt - 1/2 Sigma(N)(j=1) (B-j(n)(t))X-2(n)(t) dt = Sigma(N)(j=1) B-j(n)(t)X-n(t)d beta(n)(j)(t) + f(n)(t)dt, X-n(0) = x, where beta(n)(j) is a regular approximation of a Brownian motion beta(j), B-j(n)(t) is a family of linear continuous operators from V to H strongly convergent to B-j(t), A(n)(t) -> A(t), {A(n)(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 d X(t) + A(t)X(t) dt - 1/2 Sigma(N)(j=1) B-j(2)(t)X(t) dt = Sigma(N)(j=1) B-j(t)X(t) d beta(j)(t) + f(t) dt, X(0) = x. Here V subset of H congruent to H' subset of 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 = Sigma(N)(j=1) B-j(t)Y(t) o d beta(j)(t) + f(t) dt. (C) 2012 Elsevier B.V. All rights reserved.

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