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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

XLVII: 16, 299-320, LNM 2137 (2015)

**FITZSIMMONS, Pat**; **LE JAN, Yves**; **ROSEN, Jay**

Loop Measures Without Transition Probabilities

Nature: Original

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

Retrieve article from Numdam

XV: 21, 290-306, LNM 850 (1981)

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,

Keywords: Spatial trajectories

Nature: Original

Retrieve article from Numdam

XV: 22, 307-310, LNM 850 (1981)

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

Retrieve article from Numdam

XXI: 10, 176-190, LNM 1247 (1987)

Temps local et superchamp

Retrieve article from Numdam

XXII: 18, 175-185, LNM 1321 (1988)

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)

Simultaneous boundary hitting for a two point reflecting Brownian motion

Retrieve article from Numdam

XXXV: 16, 206-219, LNM 1755 (2001)

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)

Enroulements browniens et subordination dans les groupes de Lie

XLVII: 16, 299-320, LNM 2137 (2015)

Loop Measures Without Transition Probabilities

Nature: Original