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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Adding and subtracting jumps from Markov processes


Author: Richard F. Bass
Journal: Trans. Amer. Math. Soc. 255 (1979), 363-376
MSC: Primary 60J25
DOI: https://doi.org/10.1090/S0002-9947-1979-0542886-X
MathSciNet review: 542886
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Abstract: If $ {X_t}$ is a continuous Markov process with infinitesimal generator A, if n is a kernel satisfying certain conditions, and if B is an operator given by

$\displaystyle Bg(x)\, = \,\int {[ {g( y)\, - \,g(x)}]} \,n({x,\,dy}),$

then $ A\, + \,B$ will be the generator of a Markov process that has Lévy system $ (n,\,dt)$. Conversely, if $ {X_t}$ has Lévy system $ (n,\,dt)$, n satisfies certain conditions, and B is defined as above, then $ A\, - \,B$ will be the generator of a continuous Markov process.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1979-0542886-X
Keywords: Jump processes, Hunt processes, Lévy systems, semigroups, infinitesimal generators
Article copyright: © Copyright 1979 American Mathematical Society

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