Operators associated with multi-parameter families of probability measures. (English) Zbl 1199.35411
Bakry, D. (ed.) et al., Potential theory and stochastics in Albac. Aurel Cornea memorial volume. Conference proceedings, Albac, Romania, September 4–8, 2007. Bucharest: Theta (ISBN 978-973-87899-5-1). Theta Series in Advanced Mathematics 11, 157-172 (2009).
Summary: In this paper we outline that large classes of partial differential operators and pseudodifferential operators of higher order (and with multiple characteristics) are naturally associated with certain multi-parameter families of probability measures. In certain cases these families are related to multi-parameter Markov processes. In other cases a change of variables in the parameter domain may lead to multiparameter processes. Various examples are discussed.
For the entire collection see [Zbl 1170.60002].
For the entire collection see [Zbl 1170.60002].
MSC:
| 35S10 | Initial value problems for PDEs with pseudodifferential operators |
| 47F05 | General theory of partial differential operators |
| 47G30 | Pseudodifferential operators |
| 47D07 | Markov semigroups and applications to diffusion processes |
| 60G60 | Random fields |
