Marches aléatoires, mouvement brownien et processus de branchement
Marked excursions and random trees
Markov processes and convex minorants
Martingales browniennes et conjecture de Sakai
Martingales locales et théorème de Girsanov dans les espaces de Hilbert réels séparables
Maximal brownian motions
Let Z=(X, Y) be a planar brownian motion, the filtration it generates, andBa linear brownian motion in the filtration . One says thatB(or its filtration) is maximal if no other linear -brownian motion has a filtration strictly bigger than that ofB. For instance, it is shown in [In Séminaire de Probabilités XLI 265–278 (2008) Springer] that B is maximal if there exists a linear brownian motion C independent of B and such that the planar brownian motion (B, C) generates the same filtration asZ....
Maximal inequalities for Bessel processes.
Maximum of Dyson Brownian motion and non-colliding systems with a boundary.
Mean values and harmonic functions.
Means in complete manifolds: uniqueness and approximation
Let M be a complete Riemannian manifold, M ∈ ℕ and p ≥ 1. We prove that almost everywhere on x = (x1,...,xN) ∈ MN for Lebesgue measure in MN, the measure μ ( x ) = 1 N ∑ k = 1 N δ x k has a uniquep–mean ep(x). As a consequence, if X = (X1,...,XN) is a MN-valued random variable with absolutely continuous law, then almost surely μ(X(ω)) has a unique p–mean. In particular if (Xn)n ≥ 1 is an independent sample of an absolutely continuous law in M, then the process ep,n(ω) = ep(X1(ω),...,Xn(ω)) is...
Measures charging no polar sets and additive functional of Brownian motion.
Mesure de Hausdorff de la trajectoire de certains processus à accroissements indépendants et stationnaires
Meyer's topology and brownian motion in a composite medium
Micro tangent sets of continuous functions
Motivated by the concept of tangent measures and by H. Fürstenberg’s definition of microsets of a compact set we introduce micro tangent sets and central micro tangent sets of continuous functions. It turns out that the typical continuous function has a rich (universal) micro tangent set structure at many points. The Brownian motion, on the other hand, with probability one does not have graph like, or central graph like micro tangent sets at all. Finally we show that at almost all points Takagi’s...
Minkowski sums and Brownian exit times
If is a domain in R the Brownian exit time of is denoted by Given domains and in R this paper gives an upper bound of the distribution function of when the distribution functions of and are known. The bound is sharp if and are parallel affine half-spaces. The paper also exhibits an extension of the Ehrhard inequality
Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks.
Moderate deviations and laws of the iterated logarithm for the volume of the intersections of Wiener sausages.
Moments of gamma type and the Brownian supremum process area.
Moments of passage times for Lévy processes
Mouvement brownien et inégalité de Hardy dans