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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/8980

Title: FRACTIONAL CAUCHY PROBLEMS ON BOUNDED DOMAINS
Authors: MEERSCHAERT, MM
NANE, E
VELLAISAMY, P
Keywords: time random-walks
brownian-motion
diffusion
equation
Issue Date: 2009
Publisher: INST MATHEMATICAL STATISTICS
Citation: ANNALS OF PROBABILITY, 37(3), 979-1007
Abstract: Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain D subset of R(d) with Dirichlet boundary conditions. Stochastic solutions are constructed via an inverse stable subordinator whose scaling index corresponds to the order of the fractional time derivative. Dirichlet problems corresponding to iterated Brownian motion in a bounded domain are then solved by establishing a correspondence with the case of a half-derivative in time.
URI: http://dx.doi.org/10.1214/08-AOP426
http://dspace.library.iitb.ac.in/xmlui/handle/10054/8980
http://hdl.handle.net/10054/8980
ISSN: 0091-1798
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