Application of the sector condition to the classification of sub-Markovian semigroups
Open Access
- 1 January 1978
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 244, 103-146
- https://doi.org/10.1090/s0002-9947-1978-0506612-1
Abstract
Let p t {p_{t}} , t > 0 t > 0 , be a strongly continuous submarkovian semigroup on a real Hilbert space L 2 ( X , m ) {L^2}(X, m) . The measure m is assumed to be excessive and the L 2 {L^2} generator A is assumed to satisfy an estimate (the sector condition) which permits the application of Dirichlet spaces (not necessarily symmetric). Other submarkovian semigroups P t ∼ P_t^ \sim with the same local generator and cogenerator and relative to which m is again excessive are classified in terms of generators for processes which live on a suitable boundary.Keywords
This publication has 19 references indexed in Scilit:
- Potential theory of symmetric markov processes and its applicationsPublished by Springer Nature ,1976
- Processus de Markov associé a une forme de Dirichlet non symétriqueProbability Theory and Related Fields, 1975
- On the generation of Markov processes by symmetric formsPublished by Springer Nature ,1973
- Dirichlet Spaces and Strong Markov ProcessesTransactions of the American Mathematical Society, 1971
- Regular Representations of Dirichlet SpacesTransactions of the American Mathematical Society, 1971
- Symmetric Stable Processes as Traces of Degenerate Diffusion ProcessesTheory of Probability and Its Applications, 1969
- On boundary conditions for multi-dimensional Brownian motions with symmetric resolvent densitiesJournal of the Mathematical Society of Japan, 1969
- Probability and PotentialsMathematics of Computation, 1967
- Lectures on Elliptic Boundary Value Problems.The American Mathematical Monthly, 1966
- Some Theorems Concerning 2-Dimensional Brownian MotionTransactions of the American Mathematical Society, 1958