In this paper, we establish sharp two-sided estimates for the Green functions of relativistic stable processes (i.e. Green functions for non-local operators m-(m2/[alpha]-[Delta])[alpha]/2) in half-space-like C1,1 open sets. The estimates are uniform in m[set membership, variant](0,M] for each...

We consider the Cramér-Lundberg model with investments in an asset with large volatility, where the premium rate is a bounded nonnegative random function ct and the price of the invested risk asset follows a geometric Brownian motion with drift a and volatility [sigma]0. It is proved by...

In this paper, we give rates of convergence for minimal distances between linear statistics of martingale differences and the limiting Gaussian distribution. In particular the results apply to the partial sums of (possibly long range dependent) linear processes, and to the least squares...

Iterated Bessel processes R[gamma](t),t0,[gamma]0 and their counterparts on hyperbolic spaces, i.e. hyperbolic Brownian motions Bhp(t),t0 are examined and their probability laws derived. The higher-order partial differential equations governing the distributions of and are obtained and...

We use integration by parts formulas to give estimates for the Lp norm of the Riesz transform. This is motivated by the representation formula for conditional expectations of functionals on the Wiener space already given in Malliavin and Thalmaier (2006) [13]. As a consequence, we obtain...

The problem of estimating the Lévy density of a partially observed multidimensional affine process from low-frequency and mixed-frequency data is considered. The estimation methodology is based on the log-affine representation of the conditional characteristic function of an affine process and...

We construct optimal Markov couplings of Lévy processes, whose Lévy (jump) measure has an absolutely continuous component. The construction is based on properties of subordinate Brownian motions and the coupling of Brownian motions by reflection.

We study the path behaviour of general random walks, and that of their local times, on the 2-dimensional comb lattice that is obtained from by removing all horizontal edges off the x-axis. We prove strong approximation results for such random walks and also for their local times. Concentrating...

Given a filtered probability space , an -adapted continuous increasing process [Lambda] and a positive local martingale N such that satisfies Zt<=1,t>=0, we construct probability measures and a random time [tau] on an extension of , such that the survival probability of [tau], i.e., is equal to Zt for...</=1,t>

In this paper, we establish the existence and uniqueness of solutions of systems of stochastic partial differential equations (SPDEs) with reflection in a convex domain. The lack of comparison theorems for systems of SPDEs makes things delicate.