Question: Suppose X t solves d X t = g ( X t , t ) d t + g ( X t , t )

SupposeXt solves dXt=g(Xt,t)dt+g(Xt,t)dWt,X0=x whereg(x,t) satisfies the ordinary differential equation gt+21g2gxx=0. Find the stochastic differential equation for the process g(Xt,t). Show thatg(x,t)=hx(h1(x,t),t) whereh(x,t) solvesht+21hxx=0 and solve the corresponding stochastic differential equation.

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