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Some Solutions of Semilinear Stochastic Equations in a Hilbert Space With a Fractional Brownian Motion

机译：分数布朗运动的希尔伯特空间中半线性随机方程的一些解

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Stochastic equations in a Hilbert space with a fractional Brownian motion are used to model stochastic partial differential equations with a space-time noise. Some semilinear stochastic equations are shown to possess one and only one weak solution. These weak solutions are constructed from the solutions of the corresponding linear equations by an absolutely continuous transformation of measures. Some examples of stochastic differential and partial differential equations are given to demonstrate the applicability of the results

机译：具有分数布朗运动的希尔伯特空间中的随机方程用于对具有时空噪声的随机偏微分方程建模。一些半线性随机方程显示只有一个弱解。通过对测量值进行绝对连续的变换，从相应线性方程的解中构造出这些弱解。给出了一些随机微分方程和偏微分方程的例子，以证明结果的适用性

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《》|2006年|3077-3082|共6页
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Duncan; T.E.; Maslowski; B.; Pasik-Duncan; B.;
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Brownian motion; Hilbert spaces; partial differential equations; stochastic systems; Hilbert space; fractional Brownian motion; linear equations; semilinear stochastic equations; space-time noise; stochastic differential equations; stochastic partial differential e;

机译：布朗运动;希尔伯特空间;偏微分方程;随机系统;希尔伯特空间;分数布朗运动;线性方程;半线性随机方程;时空噪声;随机微分方程;随机偏微分e;

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专利

1. SEMILINEAR STOCHASTIC EQUATIONS IN A HILBERT SPACE WITH A FRACTIONAL BROWNIAN MOTION [J] . Duncan TE, Maslowski B, Pasik-Duncan B SIAM Journal on Mathematical Analysis . 2009,第6期

机译：分数阶布朗运动的希尔伯特空间中的半线性随机方程
2. Approximate controllability of fractional neutral stochastic evolution equations in Hilbert spaces with fractional Brownian motion [J] . Mourad Kerboua Stochastic Analysis and Applications . 2018,第2期

机译：分数布朗运动的希尔伯特空间中分数中立随机演化方程的近似可控性
3. SOME LINEAR-QUADRATIC STOCHASTIC DIFFERENTIAL GAMES FOR EQUATIONS IN HILBERT SPACES WITH FRACTIONAL BROWNIAN MOTIONS [J] . TYRONE E. DUNCAN Discrete and continuous dynamical systems . 2015,第11期

机译：具有分数布朗运动的希尔伯特空间方程组的一些线性二次随机微分游戏
4. Some Solutions of Semilinear Stochastic Equations in a Hilbert Space With a Fractional Brownian Motion [C] . T. E. Duncan, B. Maslowski, B. Pasik-Duncan IEEE Conference on Decision and Control . 2006

机译：具有分数布朗运动的希尔伯特空间中半线性随机方程的一些解决方案
5. Malliavin calculus for backward stochastic differential equations and stochastic differential equations driven by fractional Brownian motion and numerical schemes. [D] . Song, Xiaoming. 2011

机译：Malliavin演算，用于分数布朗运动和数值格式驱动的后向随机微分方程和随机微分方程。
6. Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications [O] . Xiao-Li Ding, Juan J. Nieto 2018

机译：分数褐色运动及其应用驱动的多时间尺度分数随机微分方程的分析解
7. SEMILINEAR STOCHASTIC EQUATIONS IN A HILBERT SPACE WITH A FRACTIONAL BROWNIAN MOTION [O] . T. E. Duncan, B. Maslowski, B. Pasik-duncan 2010

机译：分数阶布朗运动的希尔伯特空间中的半线性随机方程

Some Solutions of Semilinear Stochastic Equations in a Hilbert Space With a Fractional Brownian Motion

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