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8 matches found
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 formula
Nature: Original
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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 trajectories
Nature: Original
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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 theory
Nature: Original
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XXI: 10, 176-190, LNM 1247 (1987)
LE JAN, Yves
Temps local et superchamp
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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
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XXIII: 19, 234-238, LNM 1372 (1989)
CRANSTON, Michael; LE JAN, Yves
Simultaneous boundary hitting for a two point reflecting Brownian motion
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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
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XXXIX: 17, 357-380, LNM 1874 (2006)
ENRIQUEZ, Nathanaël; FRANCHI, Jacques; LE JAN, Yves
Enroulements browniens et subordination dans les groupes de Lie