gogo

y(X) = exp(2X) => dy=(exp(2X))*2*dx=y*2*dx=2ydx => dy/2y=-(sigma^2)*(1/y) + 2*sigma*y^(-1/2) * dWt dy = -2(sigma^2) + 4*sigma*y^(1/2)dWt

the result of that is: dy = - (sigma^2)dt + 4*sigma*y^(1/2)dWt i dont know, i dont think there's an explicit solution for "my" SDE (My apologies for not writing in Latex)

could you give me the exact solution for X(t) from that?? With some supstitutions i've came to the ekvivalent SDE to the first one I posted: dY(t) = -(0.5*sigma^2)*(1/Y(t))dt + 2*sigma*dW(t) (suptitution is: Y(t) = exp( X(t) )

o is actualy greek simbol "sigma" but i cant write it on my computer W represents Brown's movement SDE is a stohastic differential equation I was hoping that someone with experiance in solving this could help me

the problem just states that that by using Ito's formula on function F(t,x)=exp(x) you must find an explicit term(or formula,i'm not sure which word to us) for proces (X(t) )

Hello Could someone help me solving this SDE dX(t) = -0.5*o^2*exp( -2*X(t) )dt + 2*o*exp( -X(t) )dWt by using Itos formula on function F(t,x)=exp(x) It is quite urgent and I would apriciete Your solution Thank you