In standard calculus it is a well known fact that left-point and mid-point Riemann sums do become equal in the limit. When it comes to stochastic integration this is no longer the …

Could anyone give me some references where I could find (a) discrete version(s) of Ito's lemma (b) a proof how it converges to the continuous form in the limit (c) its usage within …

I know that Paul Malliavin was heavily influenced by ideas from differential geometry while developing his calculus on Wiener space. But what are the concrete analogies between bot …

Hi, probably this is a fairly newbie question, but is it possible that the a generic Levy process explodes (i.e. tends to infinity for finite time t with positive probability)? I …

In Wiersema: Brownian Motion Calculus on p. 205 (in an Annex on Moment Generating Functions (mgf)) the following equation is being presented $${d^k \over d\theta^k} \left ({1\over …

The following problem arose for my collaborators and me when studying the computational complexity of the Maximum-Cut problem. Let $f : \mathbb{R} \to \mathbb{R}$ be an odd functi …

Hi everyone, I am looking for some ideas (or references) in order to get an explicit SDE (if it exists) which would have a stylised property extending in some sense the mean-rever …

Are there any specialized Computer Algebra Systems (or packages for these) for finding closed form solutions to a) partial differential equations, b) stochastic differential equa …

Take an OU process characterized by X(0) = x dX(t) = - a X(t) dt + b dW(t) where a,b >0. The parameter a is usually interpreted a dissipative term, and b is a volatility term. …

S is a price process which follows Geometric Brownian motion with no drift: dS=S*vol*dW, vol=const., W is a Wiener process. Define the following ratio: R=E[Max(f(S)-S(T),0)]/E[f( …