Levý-Khintchine Inequalities, Multiple Reflection, and Brownian Motion

Boundary behavior of a constrained Brownian motion between reflecting-repellent walls

Stochastic variational inequalities provide a unified treatment for stochastic differential equations living in a closed domain with normal reflection and (or) singular repellent drift. When the domain is a polyhedron, we prove that the reflected-repelled Brownian motion does not hit the non-smooth part of the boundary. A sufficient condition for nonhitting a face of the polyhedron is derived f...

Isoperimetric-type inequalities for iterated Brownian motion in R

We extend generalized isoperimetric-type inequalities to iterated Brownian motion over several domains in R. These kinds of inequalities imply in particular that for domains of finite volume, the exit distribution and moments of the first exit time for iterated Brownian motion are maximized with the ball D centered at the origin, which has the same volume as D. Mathematics Subject Classificatio...

A Geometric Drift Inequality for a Reflected Fractional Brownian Motion Process on the Positive Orthant

We study a d-dimensional reflected fractional Brownian motion (RFBM) process on the positive orthant S = R+, with drift r0 ∈ R and Hurst parameter H ∈ ( 1 2 , 1). Under a natural stability condition on the drift vector r0 and reflection directions, we establish a geometric drift towards a compact set for the 1-skeleton chain Z̆ of the RFBM process Z; that is, there exist β, b ∈ (0,∞) and a compa...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

On the Khintchine and Rosenthal Inequalities in Noncommutative Symmetric Spaces

Probabilistic inequalities for independent random variables and martingales play a prominent role in many different areas of mathematical research, such as harmonic analysis, probability theory, Banach space geometry and the study of symmetric function spaces. In the recent years, many of these classical probabilistic inequalities have been generalized to the context of noncommutative Lp-spaces...