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Tribus markoviennes et prédiction

Séminaire de probabilités de Strasbourg

Martingales et changement de temps

Séminaire de probabilités de Strasbourg

Temps local et superchamp

Séminaire de probabilités de Strasbourg

Simultaneous boundary hitting for a two point reflecting brownian motion

Séminaire de probabilités de Strasbourg

Three examples of brownian flows on $ℝ$

Annales de l'I.H.P. Probabilités et statistiques

We show that the only flow solving the stochastic differential equation (SDE) on $ℝ$ $\mathrm{d}{X}_{t}={1}_{\left\{{X}_{t}gt;0\right\}}{W}^{+}\left(\mathrm{d}t\right)+{1}_{\left\{{X}_{t}lt;0\right\}}\phantom{\rule{0.166667em}{0ex}}\mathrm{d}{W}^{-}\left(\mathrm{d}t\right),$ where ${W}^{+}$ and ${W}^{-}$ are two independent white noises, is a coalescing flow we will denote by ${\varphi }^{±}$. The flow ${\varphi }^{±}$ is a Wiener solution of the SDE. Moreover, ${K}^{+}=𝖤\left[{\delta }_{{\varphi }^{±}}|{W}^{+}\right]$ is the unique solution (it is also a Wiener solution) of the SDE ${K}_{s,t}^{+}f\left(x\right)=f\left(x\right)+{\int }_{s}^{t}{K}_{s,u}\left({1}_{ℝ}^{+}{f}^{\text{'}}\right)\left(x\right){W}^{+}\left(\mathrm{d}u\right)+\frac{1}{2}{\int }_{s}^{t}{K}_{s,u}f\left(x\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}u$ for $slt;t$, $x\in ℝ$ and $f$ a twice continuously differentiable function. A third flow ${\varphi }^{+}$ can be constructed out of the $n$-point motions of ${K}^{+}$. This flow is coalescing and its $n$-point motion is given by...

Sur les trajectoires intrinsèques des processus de Markov et le théorème de Shih

Annales de l'I.H.P. Probabilités et statistiques

Stastistic of the winding of geodesics on a Riemann surface with finite area and constant negative curvature.

Revista Matemática Iberoamericana

In this paper we show that the windings of geodesics around the cusps of a Riemann surface of a finite area, behave asymptotically as independent Cauchy variables.

The statistical equilibrium of an isotropic stochastic flow with negative Lyapounov exponents is trivial

Séminaire de probabilités de Strasbourg

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