On the distribution and q-variation of the solution to the heat equation with fractional Laplacian
DOI:
https://doi.org/10.19195/0208-4147.39.2.5Słowa kluczowe:
Stochastic heat equation, fractional Brownian motion, fractional Laplacian, quadratic variationAbstrakt
We study the probability distribution of the solution to the linear stochastic heat equation with fractional Laplacian and white noise in time and white or correlated noise in space. As an application, we deduce the behavior of the q-variations of the solution in time and in space.
