Backward Stochastic partial differential equations in infinite dimensions

Abdul Rahman AL-Hussein

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Backward Stochastic partial differential equations in infinite dimensions

机译：无限维的倒向随机偏微分方程

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摘要

With respect to an arbitrary right continuous filtration, not necessary the Wiener filtration, a certain class of backward stochastic differential equations in infinite dimensions is studied. The solution of such an equation is required to be predictable and is got uniquely with the help of a martingale representation theorem which is proved as well. The second part of the paper is devoted to proving the existence and uniqueness of the solution of a backward stochastic partial differential equation.

机译：关于任意右连续过滤，而不是维纳过滤，研究了一类无穷维逆向随机微分方程。这种方程式的解必须是可预测的，并且借助于a表示定理可以得到唯一解。本文的第二部分致力于证明后向随机偏微分方程解的存在性和唯一性。

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来源
《Random operators and stochastic equations》 |2006年第1期|共22页
作者
Abdul Rahman AL-Hussein;
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正文语种 eng
中图分类随机微分方程;
关键词
MARTINGALE REPRESENTATION THEOREM; STRONG ORTHOGONALITY; BACKWARD STOCHASTIC DIFFERENTIAL EQUATION; BACKWARD STOCHASTIC PARTIAL DIFFERENTIAL EQUATION;

机译：TING表示定理;强正交性;后向随机微分方程;后向随机偏微分方程;

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2. On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations [J] . E Weinan, Hutzenthaler Martin, Jentzen Arnulf, Journal of Scientific Computing . 2019,第3期

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4. Comparison Theorems for the multi-dimensional Backward Doubly Stochastic Differential Equations [C] . Baoyan Han International Conference on Civil Engineering, Architecture and Building Materials . 2012

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5. Stochastic mesh method for high dimensional backward stochastic differential equation [D] . Yuan, Peng. 2016

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6. Infinite time interval backward stochastic differential equations with continuous coefficients [O] . Zhaojun Zong, Feng Hu -1

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7. Backward stochastic partial differential equations driven by infinite-dimensional martingales and applications [O] . Al-Hussein, AbdulRahman 2009

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Backward Stochastic partial differential equations in infinite dimensions

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