ON THE DISTRIBUTION AND -VARIATION OF THE SOLUTION TO
THE HEAT EQUATION WITH FRACTIONAL LAPLACIAN
Z. Mahdi Khalil
C. A. Tudor
Abstract: 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 -variations of the solution in time
and in space.
2000 AMS Mathematics Subject Classification: Primary: 60G15; Secondary: 60H05,
60G18.
Keywords and phrases: Stochastic heat equation, fractional Brownian motion, fractional
Laplacian, quadratic variation.