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FRACTIONAL CAUCHY PROBLEMS ON BOUNDED DOMAINS

DSpace at IIT Bombay

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Field Value
 
Title FRACTIONAL CAUCHY PROBLEMS ON BOUNDED DOMAINS
 
Creator MEERSCHAERT, MM
NANE, E
VELLAISAMY, P
 
Subject time random-walks
brownian-motion
diffusion
equation
fractional diffusion
cauchy problem
iterated brownian motion
brownian subordinator
caputo derivative
uniformly elliptic operator
bounded domain
boundary value problem
 
Description 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.
 
Publisher INST MATHEMATICAL STATISTICS
 
Date 2011-08-03T09:50:57Z
2011-12-26T12:54:09Z
2011-12-27T05:41:36Z
2011-08-03T09:50:57Z
2011-12-26T12:54:09Z
2011-12-27T05:41:36Z
2009
 
Type Article
 
Identifier ANNALS OF PROBABILITY, 37(3), 979-1007
0091-1798
http://dx.doi.org/10.1214/08-AOP426
http://dspace.library.iitb.ac.in/xmlui/handle/10054/8980
http://hdl.handle.net/10054/8980
 
Language en