Pseudo differential operators with negative definite symbols and the martingale problem
Author:
- 1 December 1995
- journal article
- research article
- Published by Taylor & Francis in Stochastics and Stochastic Reports
- Vol. 55 (3-4) , 225-252
Abstract
Pseudo differential operators with negative definite symbols p(x,ξ) arise as generators of Markov processes in a natural way. In this article we solve the martingale problem for this class of operators supposing only some boundedness condition for the symbol and prove uniqueness of the solution under the assumption that the symbol is sufficiently smooth with respect to x and comparable with a fixed negative definite function in a suitable wayKeywords
This publication has 13 references indexed in Scilit:
- The martingale problem for a class of pseudo differential operatorsMathematische Annalen, 1994
- A class of Feller semigroups generated by pseudo differential operatorsMathematische Zeitschrift, 1994
- Pseudo differential operators with variable order of differentiation generating feller semigroupsIntegral Equations and Operator Theory, 1993
- Further pseudodifferential operators generating Feller semigroups and Dirichlet formsRevista Matemática Iberoamericana, 1993
- Some commutator estimates for pseudo differential operators with negative definite functions as symbolsIntegral Equations and Operator Theory, 1993
- Stochastic processes and semigroups associated with degenerate lévy generating operatorsStochastics and Stochastic Reports, 1989
- Uniqueness in law for pure jump Markov processesProbability Theory and Related Fields, 1988
- Pseudo-differential operators and Markov processesJournal of the Mathematical Society of Japan, 1984
- Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continuesAnnales de l'institut Fourier, 1976
- Potential Theory on Locally Compact Abelian Groups1975