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| Volume 30 • Number 2 • 2007 |
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•
Time-dependent Backward Stochastic Evolution
Equations
AbdulRahman Al-Hussein
Abstract.
We consider the following infinite dimensional backward stochastic
evolution equation:
-d Y(t) = ( A (t) Y(t) + f (t , Y(t) , Z(t) ) ) dt - Z(t) d W(t),
Y(T) = x,
where A(t) , t ≥ 0 , are unbounded operators that generate a
strong evolution operator U ( t , r), 0 ≤ r ≤ t ≤ 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.
2000 Mathematics Subject Classification: Primary 60H10, 60H15, 60H30; Secondary 47J35, 60H20
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