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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 \[ Bg(x) = \int {[ {g( y) - g(x)}]} n({x, dy}),\] 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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Keywords: Jump processes, Hunt processes, Lévy systems, semigroups, infinitesimal generators
Article copyright: © Copyright 1979 American Mathematical Society