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REFLECTED SPECTRALLY NEGATIVE STABLE PROCESSES AND THEIR GOVERNING EQUATIONS.
- Source :
- Transactions of the American Mathematical Society; Jan2016, Vol. 368 Issue 1, p227-248, 22p
- Publication Year :
- 2016
-
Abstract
- This paper explicitly computes the transition densities of a spectrally negative stable process with index greater than one, reflected at its infimum. First we derive the forward equation using the theory of sun-dual semigroups. The resulting forward equation is a boundary value problem on the positive half-line that involves a negative Riemann-Liouville fractional derivative in space, and a fractional reflecting boundary condition at the origin. Then we apply numerical methods to explicitly compute the transition density of this space-inhomogeneous Markov process, for any starting point, to any desired degree of accuracy. Finally, we discuss an application to fractional Cauchy problems, which involve a positive Caputo fractional derivative in time. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 368
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 110521109
- Full Text :
- https://doi.org/10.1090/tran/6360