Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Superprocesses and their linear additive functionals

Author: E. B. Dynkin
Journal: Trans. Amer. Math. Soc. 314 (1989), 255-282
MSC: Primary 60J80; Secondary 60G57, 60H05, 60J55
MathSciNet review: 930086
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X = ({X_t},P)$ be a measure-valued stochastic process. Linear functionals of $ X$ are the elements of the minimal closed subspace $ L$ of $ {L^2}(P)$ which contains all $ {X_t}(B)$ with $ \smallint {{X_t}{{(B)}^2}\;dP\; < \infty } $. Various classes of $ L$-valued additive functionals are investigated for measure-valued Markov processes introduced by Watanabe and Dawson. We represent such functionals in terms of stochastic integrals and we derive integral and differential equations for their Laplace transforms. For an important particular case--"weighted occupation times"--such equations have been established earlier by Iscoe.

We consider Markov processes with nonstationary transition functions to reveal better the principal role of the backward equations. This is especially helpful when we derive the formula for the Laplace transforms.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60J80, 60G57, 60H05, 60J55

Retrieve articles in all journals with MSC: 60J80, 60G57, 60H05, 60J55

Additional Information

PII: S 0002-9947(1989)0930086-7
Keywords: Measure-valued Markov processes, additive funtionals, stochastic integrals
Article copyright: © Copyright 1989 American Mathematical Society