Harmonic Analysis and nonstandard Brownian Motion in the plane.
Harmonic functions along Brownan balls an the Liouville property for solvable Lie groups.
Harmonic functions on loop groups
Harmonic measures versus quasiconformal measures for hyperbolic groups
We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.
Harnack inequality for functional sdes with bounded memory.
Hausdorff dimension of cut points for Brownian motion.
Hausdorff–Besicovitch measure of fractal functional limit laws induced by Wiener process in Hölder norms
Heat flow, brownian motion and newtonian capacity
Heat kernel measure on central extension of current groups in any dimension.
Hedging entry and exit decisions: Activating and deactivating barrier options.
Hermite and Laguerre polynomials and matrix-valued stochastic.
Hiding a constant drift
The following question is due to Marc Yor: Let B be a brownian motion and St=t+Bt. Can we define an -predictable process H such that the resulting stochastic integral (H⋅S) is a brownian motion (without drift) in its own filtration, i.e. an -brownian motion? In this paper we show that by dropping the requirement of -predictability of H we can give a positive answer to this question. In other words, we are able to show that there is a weak solution to Yor’s question. The original question, i.e.,...
Hirsch's integral test for the iterated brownian motion
Hitting a boundary point with reflected brownian motion
Hitting distributions of geometric Brownian motion
Let τ be the first hitting time of the point 1 by the geometric Brownian motion X(t) = x exp(B(t) - 2μt) with drift μ ≥ 0 starting from x > 1. Here B(t) is the Brownian motion starting from 0 with EB²(t) = 2t. We provide an integral formula for the density function of the stopped exponential functional and determine its asymptotic behaviour at infinity. Although we basically rely on methods developed in [BGS], the present paper covers the case of arbitrary drifts μ ≥ 0 and provides a significant...
Hitting probabilities and potential theory for the brownian path-valued process
We consider the Brownian path-valued process studied in [LG1], [LG2], which is closely related to super Brownian motion. We obtain several potential-theoretic results related to this process. In particular, we give an explicit description of the capacitary distribution of certain subsets of the path space, such as the set of paths that hit a given closed set. These capacitary distributions are characterized as the laws of solutions of certain stochastic differential equations. They solve variational...
Hitting probabilities of killed brownian motion : a study on geometric regularity
Hölder norms and the support theorem for diffusions