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Mixed sub-fractional-White heat equation. (English) Zbl 1360.60129

Summary: We introduce a new stochastic heat equation with a colored-white fractional noise, which behaves as a Wiener process in the spatial variable and as mixed sub-fractional Brownian motion in time. A necessary and sufficient condition for the existence of its solution is reported. We also analyze regularity properties of this equation, with respect to the temporal and spatial variables, respectively. Some fractal dimensions of the graphs and ranges of the associated sample paths are determined.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G15 Gaussian processes
60G17 Sample path properties
28A80 Fractals
80A05 Foundations of thermodynamics and heat transfer
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