期刊
STOCHASTICS AND DYNAMICS
卷 10, 期 3, 页码 341-366出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S021949371000298X
关键词
Iterated Brownian motion of Burdzy; k-iterated Brownian motion; Brownian-time Brownian motion of Allouba and Zheng; exit time; bounded domain; heat equation; Caputo fractional derivative; fractional diffusion; higher of cauchy problems
We study solutions of a class of higher order partial differential equations in bounded domains. These partial differential equations appeared first time in the papers of Allouba and Zheng [4], Baeumer, Meerschaert and Nane [10], Meerschaert, Nane and Vellaisamy [37], and Nane [42]. We express the solutions by subordinating a killed Markov process by a hitting time of a stable subordinator of index 0 < beta < 1, or by the absolute value of a symmetric alpha-stable process with 0 < alpha <= 2, independent of the Markov process. In some special cases we represent the solutions by running composition of k independent Brownian motions, called k-iterated Brownian motion for an integer k >= 2. We make use of a connection between fractional-time diffusions and higher order partial differential equations established first by Allouba and Zheng [4] and later extended in several directions by Baeumer, Meerschaert and Nane [10].
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