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Unformatted text preview: 5) Assume that X is a solution to the following SDE: dX t = b ( t,X t ) dt + σ ( t,X t ) dB t , X = x, t ≥ , and u = u ( t,x ) is a classical ( C 1 , 2 ) solution to the PDE: 0 = u t + 1 2 σ 2 ( t,x ) u xx + b ( t,x ) u x + c ( t ) u + f ( t,x ); u ( T,x ) = g ( x ) . Argue that u ( t,x ) = E n e R T t c ( s ) ds g ( X T ) + Z T t e R s t c ( r ) dr f ( s,X s ) ds ﬂ ﬂ ﬂ X t = x o . 1...
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This note was uploaded on 10/08/2010 for the course MA 503 taught by Professor Majin during the Fall '09 term at USC.
 Fall '09
 MAJIN

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