Fractional diffusion and fractional heat equation

Autor:	J. M. Angulo, M. D. Ruiz-Medina, V. V. Anh, W. Grecksch
Rok vydání:	2000
Předmět:	Statistics and Probability 010104 statistics & probability Applied Mathematics 010102 general mathematics 0101 mathematics 01 natural sciences
Zdroj:	Advances in Applied Probability. 32:1077-1099
ISSN:	1475-6064 0001-8678
DOI:	10.1017/s0001867800010478
Popis:	This paper introduces a fractional heat equation, where the diffusion operator is the composition of the Bessel and Riesz potentials. Sharp bounds are obtained for the variance of the spatial and temporal increments of the solution. These bounds establish the degree of singularity of the sample paths of the solution. In the case of unbounded spatial domain, a solution is formulated in terms of the Fourier transform of its spatially and temporally homogeneous Green function. The spectral density of the resulting solution is then obtained explicitly. The result implies that the solution of the fractional heat equation may possess spatial long-range dependence asymptotically.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ab8cf3b71b2be63b15389cc878dbcb0f https://doi.org/10.1017/s0001867800010478 Zobrazit plný text záznamu