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- aquafina123
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Ito Calculus
Hi, I have a question regarding basic Ito Calculus.I know that the useful form of Ito rule is: df = f_t*dt + f_x*dX + (1/2)*f_xx*dX*dXfor the diffusion process dX(t) = mu(t,X)dt + sigma(t,X)dW(t)However, when you have a SDE in form of dX(t) = X(t) * [mu(t,X)dt + sigma(t,X)dW(t)] and f = 1/Xhow can you apply Ito rule?Thaks a lot.
Last edited by aquafina123 on March 1st, 2010, 11:00 pm, edited 1 time in total.
Ito Calculus
QuoteOriginally posted by: aquafina123Hi, I have a question regarding basic Ito Calculus.I know that the useful form of Ito rule is: df = f_t*dt + f_x*dX + (1/2)*f_xx*dX*dXfor the diffusion process dX(t) = mu(t,X)dt + sigma(t,X)dW(t)However, when you have a SDE in form of dX(t) = X(t) * [mu(t,X)dt + sigma(t,X)dW(t)] and f = 1/Xhow can you apply Ito rule?Thaks a lot.It is completely straightforward to apply Ito's rule to your SDE.I would guess your source of confusion is that the functions mu and sigma in your SDE are not the same as the mu and sigma in Ito's rule.