A change of variable formula with Itô correction term

Mathematics – Probability

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Published in at http://dx.doi.org/10.1214/09-AOP523 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/09-AOP523

We consider the solution $u(x,t)$ to a stochastic heat equation. For fixed $x$, the process $F(t)=u(x,t)$ has a nontrivial quartic variation. It follows that $F$ is not a semimartingale, so a stochastic integral with respect to $F$ cannot be defined in the classical It\^{o} sense. We show that for sufficiently differentiable functions $g(x,t)$, a stochastic integral $\int g(F(t),t)\,dF(t)$ exists as a limit of discrete, midpoint-style Riemann sums, where the limit is taken in distribution in the Skorokhod space of cadlag functions. Moreover, we show that this integral satisfies a change of variable formula with a correction term that is an ordinary It\^{o} integral with respect to a Brownian motion that is independent of $F$.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

A change of variable formula with Itô correction term does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A change of variable formula with Itô correction term, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A change of variable formula with Itô correction term will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-303536

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.