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Time-dependent Backward Stochastic Evolution Equations

Al-Hussein, Abdul Rahman, (2007) Time-dependent Backward Stochastic Evolution Equations. Bulletin of the Malaysian Mathematical Sciences Society, 30 (2). pp. 159-183. ISSN 0126-6705

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Official URL: http://math.usm.my/bulletin/pdf/v30n2/v30n2p8.pdf

Affiliations

Al-Qassem University, College of Science, Dept. of Mathematics

Abstract

We consider the following infinite dimensional backward stochastic evolution equation: $\left \{ \begin{array}{rcl} -dY(t) = (A(t) Y(t) + f(t,Y(t),Z(t))) dt - Z(t)dW(t), \\ Y(T)=\xi, \end{array} \right$ , where $A(t),t \geq 0$, are unbounded operators that generate a strong evolution operator $U(t,r), 0 \leq r \leq t \leq T$. We prove under non-Lipschitz conditions that such an equation admits a unique evolution solution. Some examples and regularity properties of this solution are given as well.

Item Type:Journal
Keywords:Martingale representation theorem, Backward stochastic evolution equation, Evolution operator, Evolution solution.
Subjects:Q Science, Computer Science
ID Code:1452

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