Sample-path stability conditions for multiserver input-output processes.
Sampling formulae for symmetric selection.
Sauts additifs et sauts multiplicatifs des semi-martingales
Scaling limit of the prudent walk.
Scaling limit of the random walk among random traps on ℤd
Attributing a positive value τx to each x∈ℤd, we investigate a nearest-neighbour random walk which is reversible for the measure with weights (τx), often known as “Bouchaud’s trap model.” We assume that these weights are independent, identically distributed and non-integrable random variables (with polynomial tail), and that d≥5. We obtain the quenched subdiffusive scaling limit of the model, the limit being the fractional kinetics process. We begin our proof by expressing the random walk as the...
Scaling of a random walk on a supercritical contact process
We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the random walk...
Schatten classes and commutators on simple martingales
Schätzen der Kovarianzdichte stationärer Punktprozesse aus Zählungen.
Second order parabolic equations and weak uniqueness of diffusions with discontinuous coefficients
We prove the unique solvability of parabolic equations with discontinuous leading coefficients in . Using this result, we establish the uniqueness of diffusion processes with time-dependent discontinuous coefficients.
Second order stochastic processes and the dilation theory in Banach spaces
Second-order asymptotic expansion for a non-synchronous covariation estimator
In this paper, we consider the problem of estimating the covariation of two diffusion processes when observations are subject to non-synchronicity. Building on recent papers [Bernoulli11 (2005) 359–379, Ann. Inst. Statist. Math.60 (2008) 367–406], we derive second-order asymptotic expansions for the distribution of the Hayashi–Yoshida estimator in a fairly general setup including random sampling schemes and non-anticipative random drifts. The key steps leading to our results are a second-order decomposition...
Sectorial local non-determinism and the geometry of the Brownian sheet.
Selections of set-valued stochastic processes.
Self-decomposable probability measures on Banach spaces
Self-intersection local time of -superprocess
Self-repelling random walk with directed edges on Z.
Self-similar and Markov composition structures.
Self-similar fragmentations
Self-similar processes in collective risk theory.
Self-similar random fractal measures using contraction method in probabilistic metric spaces.