Functionals of Markov Processes and Superprocesses
Leviatan, Talma
Ann. Probab., Tome 3 (1975) no. 6, p. 41-48 / Harvested from Project Euclid
It is well known that a contraction multiplicative functional $\alpha_t, t \geqq 0$ on some Markov process with transition $P_t, t \geqq 0$, yields another Markov process whose semigroup $Q_t(x, A) = E_x(\alpha_t, X_t \in A)$ is subordinate to $P_t, t \geqq 0$. The second process results from the original one by adding a killing operation at a rate of $-d\alpha_t/\alpha_t$. This paper deals with expansion multiplicative functionals (satisfying $\alpha_t \geqq 1$ and $E_x(\alpha_t) < \infty)$. It is proved that such functionals yield a Markov process with creation and annihilation of mass. Relations to the original process are established. Finally the results are generalized to, so-called, conditionally monotone functionals.
Publié le : 1975-02-14
Classification:  6062,  6067,  Expansions multiplicative functionals,  dominating semigroup,  Markov processes with creation and annihilation
@article{1176996446,
     author = {Leviatan, Talma},
     title = {Functionals of Markov Processes and Superprocesses},
     journal = {Ann. Probab.},
     volume = {3},
     number = {6},
     year = {1975},
     pages = { 41-48},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996446}
}
Leviatan, Talma. Functionals of Markov Processes and Superprocesses. Ann. Probab., Tome 3 (1975) no. 6, pp.  41-48. http://gdmltest.u-ga.fr/item/1176996446/