IV: 06, 71-72, LNM 124 (1970)
DELLACHERIE, Claude
Au sujet des sauts d'un processus de Hunt (
Markov processes)
Two a.s. results on jumps: the process cannot jump
from a semi-polar set; at the first hitting time of any finely closed set $F$, either the process does not jump, or it jumps from outside $F$
Comment: Both results are improvements of previous results of Meyer and Weil
Keywords: Hunt processes,
Semi-polar setsNature: Original
Retrieve article from Numdam
IX: 34, 530-533, LNM 465 (1975)
MEYER, Paul-André
Sur la démonstration de prévisibilité de Chung et Walsh (
Markov processes)
A new proof of the result that for a Hunt process, the previsible stopping times are exactly those at which the process does not jump was given by Chung-Walsh (
Z. für W-theorie, 29, 1974). Their idea is used here in a modified way, using a formula of Dawson which ``explicitly'' computes conditional expectations and projections. Then it is extended to Ray processes
Comment: The contents of this paper became Chapter XIV
44--47 in Dellacherie-Meyer,
Probabilités et PotentielKeywords: Hunt processes,
Previsible timesNature: Exposition Retrieve article from Numdam
X: 05, 44-77, LNM 511 (1976)
KUNITA, Hiroshi
Absolute continuity for Markov processes (
Markov processes)
This paper is devoted to a ``progressive'' Lebesgue decomposition of the laws of a Markov process with respect to a second one in the same filtration, and the structure of the corresponding density. The two processes are assumed to be Hunt processes, and for part of the paper satisfy Hunt's hypothesis (K) (all excessive functions are regular, or semi-polar sets are polar). The topics discussed are the following: Lévy systems and the relation between the Lévy systems of a process and of its transform by a multiplicative functional; structure of exact perfect terminal times, which are shown to be hitting times of sets in space-time, by the process $(X_{t-},X_t)$ (a version of a result of Walsh-Weil,
Ann. Sci. ENS, 5, 1972); the ``Lebesgue decomposition'' of a Markov process with respect to another, and the fact that if absolute continuity holds on the germ field it also holds up to some maximal terminal time; a condition for this terminal time to be equal to the lifetime, under hypothesis (K)
Comment: The pasting together of the Lebesgue decompositions of a probability measure with respect to another one, on the $\sigma$-fields of a given filtration, is called the
Kunita decomposition, and is not restricted to Markov processes. For the general case, see Yoeurp, in LN
1118,
Grossissements de filtrations, 1985
Keywords: Absolute continuity of laws,
Hunt processes,
Terminal times,
Kunita decompositionNature: Original Retrieve article from Numdam
XIV: 44, 418-436, LNM 784 (1980)
RAO, Murali
A note on Revuz measure (
Markov processes,
Potential theory)
The problem is to weaken the hypotheses of Chung (
Ann. Inst. Fourier, 23, 1973) implying the representation of the equilibrium potential of a compact set as a Green potential. To this order, Revuz measure techniques are used, and interesting auxiliary results are proved concerning the Revuz measures of natural additive functionals of a Hunt process
Keywords: Revuz measures,
Additive functionals,
Hunt processes,
Equilibrium potentialsNature: Original Retrieve article from Numdam
XLIV: 04, 75-103, LNM 2046 (2012)
QIAN, Zhongmin;
YING, Jiangang
Martingale representations for diffusion processes and backward stochastic differential equations (
Stochastic calculus)
Keywords: Backward Stochastic Differential equations,
Dirichlet forms,
Hunt processes,
Martingales,
Natural filtration,
Non-linear equationsNature: Original
