Adding and subtracting jumps from Markov processes

Bass, Richard F.

doi:10.1090/S0002-9947-1979-0542886-X

Adding and subtracting jumps from Markov processes
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by Richard F. Bass PDF

Trans. Amer. Math. Soc. 255 (1979), 363-376 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.

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