Maximal Inequalities for Stochastic Integrals
Maximal Weak-Type Inequality for Orthogonal Harmonic Functions and Martingales
Assume that u, v are conjugate harmonic functions on the unit disc of ℂ, normalized so that u(0) = v(0) = 0. Let u*, |v|* stand for the one- and two-sided Brownian maxima of u and v, respectively. The paper contains the proof of the sharp weak-type estimate ℙ(|v|* ≥ 1)≤ (1 + 1/3² + 1/5² + 1/7² + ...)/(1 - 1/3² + 1/5² - 1/7² + ...) 𝔼u*. Actually, this estimate is shown to be true in the more general setting of differentially subordinate harmonic functions defined...
Métrisabilité de quelques espaces de processus aléatoires
Minimization of the Kullback information for some Markov processes
Minimization of the Kullback information of diffusion processes
Moderate deviations for martingales with bounded jumps.
Modifications : “Some invariance properties (of the laws) of Ocone's martingales”
Multifractal analysis of infinite products of stationary jump processes.
Multiplications aléatoires et dimensions de Hausdorff
Multiplicative decomposition of nonsingular matrix valued semimartingales