Stochastic differential equation driven by the Wiener process in a Banach space, existence and uniqueness of the generalized solution

Badri Mamporia

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Stochastic differential equation driven by the Wiener process in a Banach space, existence and uniqueness of the generalized solution

机译：Banach空间中由Wiener过程驱动的随机微分方程，广义解的存在性和唯一性

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In this paper the stochastic differential equation in a Banach space is considered for the case when the Wiener process in the equation is Banach space valued and the integrand non-anticipating function is operator-valued. At first the stochastic differential equation for the generalized random process is introduced and developed existence and uniqueness of solutions as the generalized random process. The corresponding results for the stochastic differential equation in a Banach space is given. In [5] we consider the stochastic differential equation in a Banach space in the case, when the Wiener process is one dimensional and the integrand non-anticipating function is Banach space valued.

机译：在本文中，当方程中的维纳过程为Banach空间值且被积非预期函数为算子值时，考虑Banach空间中的随机微分方程。首先介绍了广义随机过程的随机微分方程，并将其发展为广义随机过程的解的存在性和唯一性。给出了Banach空间中随机微分方程的相应结果。在[5]中，当维纳过程为一维且被积非预期函数为Banach空间值时，我们考虑Banach空间中的随机微分方程。

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《Pure and Applied Mathematics Journal》 |2015年第3期|共6页
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Badri Mamporia;
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Stochastic differential equation driven by the Wiener process in a Banach space, existence and uniqueness of the generalized solution

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