Variations of the solution to a stochastic heat equation

Details Variations of the solution to a stochastic heat equation Variations of the solution to a stochastic heat equation

2005-12-31

arxiv.org/abs/math/0601007v3

Annals of Probability 2007, Vol. 35, No. 6, 2122-2159

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/009117907000000196 the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117907000000196

We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, $F(t)$, has a nontrivial quartic variation. This process, therefore, has infinite quadratic variation and is not a semimartingale. It follows that the classical It\^{o} calculus does not apply. Motivated by heuristic ideas about a possible new calculus for this process, we are led to study modifications of the quadratic variation. Namely, we modify each term in the sum of the squares of the increments so that it has mean zero. We then show that these sums, as functions of $t$, converge weakly to Brownian motion.

Affiliated with

Also associated with

No associations

Rating

Variations of the solution to a stochastic heat equation 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 Variations of the solution to a stochastic heat equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Variations of the solution to a stochastic heat equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-398900