XIII: 33, 385-399, LNM 721 (1979)
LE JAN, Yves
Martingales et changement de temps (
Martingale theory,
Markov processes)
The first part of the paper concerns changes of time by a continuous (not strictly increasing) process, with a detailed computation, for instance, of the continuous martingale part of a time-changed martingale. This is a useful addition to
1108 and
1109. The second part is an application to classical potential theory: the martingale is a harmonic function along Brownian motion in a domain, stopped at the boundary; the change of time is defined by a boundary local time. Then the time-changed Brownian motion is a Markov process on the boundary, the time-changed martingale is purely discontinuous, and the computation of its quadratic norm leads to the Douglas formula, which expresses the Dirichlet integral of the harmonic function by a quadratic double integral of its restriction to the boundary
Keywords: Changes of time,
Energy,
Douglas formulaNature: Original
Retrieve article from Numdam
XV: 21, 290-306, LNM 850 (1981)
CHACON, Rafael V.;
LE JAN, Yves;
WALSH, John B.
Spatial trajectories (
Markov processes,
General theory of processes)
It is well known that Markov processes with the same excessive functions are the same up to a strictly increasing continuous time-change. It is therefore natural to study spatial trajectories, i.e., trajectories up to a strictly increasing continuous time changes, and in particular to provide the space of all spatial trajectories with a reasonable $\sigma$-field so that it may carry measures. It is shown here that the space of right-continuous spatial trajectories with left-hand limits is a Blackwell space. The class of intrinsic stopping times defined on this space is also investigated
Comment: See Chacon-Jamison,
Israel J. of M.,
33, 1979
Keywords: Spatial trajectoriesNature: Original Retrieve article from Numdam
XV: 22, 307-310, LNM 850 (1981)
LE JAN, Yves
Tribus markoviennes et prédiction (
Markov processes,
General theory of processes)
The problem discussed here is whether a given filtration is generated by a Ray process. The answer is positive under very general conditions. Knight's prediction theory (
1007) is used
Keywords: Prediction theoryNature: Original Retrieve article from Numdam
XXI: 10, 176-190, LNM 1247 (1987)
LE JAN, Yves
Temps local et superchamp Retrieve article from Numdam
XXII: 18, 175-185, LNM 1321 (1988)
DARLING, Richard W.R.;
LE JAN, Yves
The statistical equilibrium of an isotropic stochastic flow with negative Lyapounov exponents is trivial Retrieve article from Numdam
XXIII: 19, 234-238, LNM 1372 (1989)
CRANSTON, Michael;
LE JAN, Yves
Simultaneous boundary hitting for a two point reflecting Brownian motion Retrieve article from Numdam
XXXV: 16, 206-219, LNM 1755 (2001)
ENRIQUEZ, Nathanaël;
FRANCHI, Jacques;
LE JAN, Yves
Canonical lift and exit law of the fundamental diffusion associated with a Kleinian group Retrieve article from Numdam
XXXIX: 17, 357-380, LNM 1874 (2006)
ENRIQUEZ, Nathanaël;
FRANCHI, Jacques;
LE JAN, Yves
Enroulements browniens et subordination dans les groupes de Lie
XLVII: 16, 299-320, LNM 2137 (2015)
FITZSIMMONS, Pat;
LE JAN, Yves;
ROSEN, Jay
Loop Measures Without Transition ProbabilitiesNature: Original
