Naslov
On purely discontinuous additive functionals of subordinate Brownian motions

Autori
Vondraček, Zoran ; Wagner, Vanja

Izvornik
Stochastic processes and their applications (0304-4149) 128 (2018), 2; 707-726

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Additive functionals, subordinate Brownian motion, purely discontinuous Girsanov transform, absolute continuity, singularity, relative entropy.

Sažetak
Let $A_t=\sum_{; ; ; s\le t}; ; ; F(X_{; ; ; s-}; ; ; , X_s)$ be a purely discontinuous additive functional of a subordinate Brownian motion $X=(X_t, \P_x)$. We give a sufficient condition on the non-negative function $F$ that guarantees that finiteness of $A_{; ; ; \infty}; ; ; $ implies finiteness of its expectation. This result is then applied to study the relative entropy of $\P_x$ and the probability measure induced by a purely discontinuous Girsanov transform of the process $X$. We prove these results under the weak global scaling condition on the Laplace exponent of the underlying subordinator.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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