EXPANSION THEOREMS FOR GENERALIZED RANDOM PROCESSES, WICK PRODUCTS AND APPLICATIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS

STEVAN PILIPOVIC; DORA SELESI

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EXPANSION THEOREMS FOR GENERALIZED RANDOM PROCESSES, WICK PRODUCTS AND APPLICATIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS

机译：广义随机过程，毛细积的扩展定理及其在随机微分方程中的应用

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A new Gel'fand triple exp(S)1 C (L)2 C exp(S)-1 is constructed as extension of the known Kondratiev one (S)1 C (L)2 C (S)-1. Expansion theorems for generalized stochastic processes considered as elements of the spaces L(A,(S)-1) and L(A,exp(S)-1) are derived. This series expansion is used for solving a class of evolution stochastic differential equations. The Wick product is developed on the spaces exp(S)-1, L(A(S)-1) and L(A,exp(S)-1). The series expansion of generalized stochastic processes is used for solving a class of nonlinear stochastic differential equations by means of Wick products.

机译：作为已知的Kondratiev一（S）1 C（L）2 C（S）-1的扩展，构造了新的Gel'fand三重exp（S）1 C（L）2 C exp（S）-1。推导了被认为是空间L（A，（S）-1）和L（A，exp（S）-1）的元素的广义随机过程的展开定理。该级数展开用于求解一类演化随机微分方程。 Wick产品在空间exp（S）-1，L（A（S）-1）和L（A，exp（S）-1）上展开。广义随机过程的级数展开用于利用Wick乘积求解一类非线性随机微分方程。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2007年第1期|共32页
作者
STEVAN PILIPOVIC; DORA SELESI;
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原文格式 PDF
正文语种 eng
中图分类物理学;
关键词
Generalized random process; white noise; series expansion; Wick product;

机译：广义随机过程;白噪声;级数展开;芯产品;

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1. EXPANSION THEOREMS FOR GENERALIZED RANDOM PROCESSES, WICK PRODUCTS AND APPLICATIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS [J] . STEVAN PILIPOVIC, DORA SELESI Infinite dimensional analysis, quantum probability, and related topics . 2007,第1期

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2. Reply to comment by D.-H. Lim on 'Diffusion processes in composite porous media and their numerical integration by random walks: Generalized stochastic differential equations with discontinuous coefficients' [J] . E. M. LaBolle, Yong Zhang Water resources research . 2006,第2期

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5. SOME LIMIT THEOREMS FOR STOCHASTIC DELAY-DIFFERENTIAL EQUATIONS WITH APPLICATIONS TO THEORETICAL ECOLOGY [D] . WHITE, BENJAMIN STEVEN. 1974

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6. On random fixed point theorems with applications to integral equations [O] . Kanayo Stella Eke, Hudson Akewe, Sheila Amina Bishop 2019

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EXPANSION THEOREMS FOR GENERALIZED RANDOM PROCESSES, WICK PRODUCTS AND APPLICATIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS

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