Adding and subtracting jumps from Markov processes
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 by Richard F. Bass PDF
 Trans. Amer. Math. Soc. 255 (1979), 363376 Request permission
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.References

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Additional Information
 © Copyright 1979 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 255 (1979), 363376
 MSC: Primary 60J25
 DOI: https://doi.org/10.1090/S0002994719790542886X
 MathSciNet review: 542886