Stationary and isotropic iteration stable random tessellations are considered, which are constructed by a random process of iterative cell division. The collection of maximal polytopes at a fixed time t within a convex window is regarded and formulas for mean values, variances and a...

We consider local martingales of exponential form or where X denotes one component of a multivariate affine process in the sense of Duffie et al. (2003) [8]. By completing the characterization of conservative affine processes in [8, Section 9], we provide deterministic necessary and...

By using absolutely continuous lower bounds of the Lévy measure, explicit gradient estimates are derived for the semigroup of the corresponding Lévy process with a linear drift. A derivative formula is presented for the conditional distribution of the process at time t under the condition that...

This paper is devoted to solving one-dimensional backward stochastic differential equations (BSDEs), where the time horizon may be finite or infinite and the assumptions on the generator g are not necessary to be uniform on t. We first show the existence of the minimal solution for this kind of...

We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards. Our development is presented in two parts. In the first part, we will develop the...

Given a Markovian Brownian martingale Z, we build a process X which is a martingale in its own filtration and satisfies X1=Z1. We call X a dynamic bridge, because its terminal value Z1 is not known in advance. We compute its semimartingale decomposition explicitly under both its own filtration...

We consider a model homogenization problem for the Poisson equation in a domain with a rapidly oscillating boundary which is a small random perturbation of a fixed hypersurface. A Fourier boundary condition with random coefficients is imposed on the oscillating boundary. We derive the effective...

Stochastic networks with time varying arrival and service rates and routing structure are studied. Time variations are governed by, in addition to the state of the system, two independent finite state Markov processes X and Y. The transition times of X are significantly smaller than typical...

This paper describes the limiting behaviour of tail empirical processes associated with long memory stochastic volatility models. We show that such a process has dichotomous behaviour, according to an interplay between the Hurst parameter and the tail index. On the other hand, the tail empirical...

For Lp convergence rates of a time homogeneous Markov process, sufficient conditions are given in terms of an exponential [phi]-coupling. This provides sufficient conditions for Lp convergence rates and related spectral and functional properties (spectral gap and Poincaré inequality) in terms...