Zili, M. Mixed sub-fractional-White heat equation. (English) Zbl 1360.60129 J. Numer. Math. Stoch. 8, No. 1, 17-35 (2016). 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. Cited in 1 Document 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 Keywords:mixed sub-fractional Brownian motion; stochastic heat equation; Gaussian noise; fractal dimension PDFBibTeX XMLCite \textit{M. Zili}, J. Numer. Math. Stoch. 8, No. 1, 17--35 (2016; Zbl 1360.60129) Full Text: Link