Fractional kinetic equations driven by Gaussian or infinitely divisible noise
- 1 June 2005
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 37 (2), 366-392
- https://doi.org/10.1239/aap/1118858630
Abstract
In this paper, we consider a certain type of space- and time-fractional kinetic equation with Gaussian or infinitely divisible noise input. The solutions to the equation are provided in the cases of both bounded and unbounded domains, in conjunction with bounds for the variances of the increments. The role of each of the parameters in the equation is investigated with respect to second- and higher-order properties. In particular, it is shown that long-range dependence may arise in the temporal solution under certain conditions on the spatial operators.Keywords
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