Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions

Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions

The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded operator acting on the Y...

Stochastic Differential Equations in Infinite Dimensions

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Approximate Controllability Results for Impulsive Linear Fuzzy Stochastic Differential Equations under Nonlocal Conditions

In this paper, the approximate controllability of impulsive linear fuzzy stochastic differential equations with nonlocal conditions in Banach space is studied. By using the Banach fixed point theorems, stochastic analysis, fuzzy process and fuzzy solution, some sufficient conditions are given for the approximate controllability of the system.

Approximate Boundary Controllability for Semilinear Delay Differential Equations

Yamada-watanabe Theorem for Stochastic Evolution Equations in Infinite Dimensions

The purpose of this note is to give a complete and detailed proof of the fundamental Yamada-Watanabe Theorem on infinite dimensional spaces, more precisely in the framework of the variational approach to stochastic partial differential equations. 1. Framework and Definitions Let H be a separable Hilbert space, with inner product 〈·, ·〉H and norm ‖·‖H . Let V,E be separable Banach spaces with no...