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Exercise 5.12 Consider the following boundary value problem in the domain [0,T] X R. (9F 3F 1 (PF | ,u(t,:r)a | o2(t,;1:) l T(t,;1: 0, a: at 635:2...

stochastic problem, boundary problem. Maybe I should figure out dz first, but how?

Screen Shot 2018-03-29 at 11.41.39 AM.png

Screen Shot 2018-03-29 at 11.41.39 AM.png

Exercise 5.12 Consider the following boundary value problem in the domain
[0,T] X R. (9F 3F 1 (PF
— —|— ,u(t,:r)a— —|— §o2(t,;1:)— —l— T(t,;1:)F : 0,
a: at 635:2
F(T,$) : @(gr). Here #05, :13), 0(t, 3:), r05, :17) and @(gr) are assumed to be known functions. Prove
that this problem has a stochastic representation formula of the form F(t, 2:) : Em: [©(XT)eLTT(SsXa)dS] , by considering the process ZS : F (s,Xs) >< exp U: r(u,Xu)du] on the time
interval [t,T].

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