Empirical processes indexed by classes of functions based on dependent observations are considered. Sufficient conditions in order to satisfy stochastic equicontinuity are given. The derived conditions are in terms of bracketing numbers with respect to a norm arising from a Rosenthal type moment...

We consider an affine term structure model of interest rates, where the factors satisfy a linear diffusion equation. We assume that the information available to an agent comes from observing the yields of a finite number of traded bonds and that this information is not sufficient to reconstruct...

In this paper we present sufficient conditions for the Doeblin decomposition, and necessary and sufficient conditions for an ergodic decomposition for a Markov chain satisfying a T'-condition, which is a condition adapted from the paper (Statist. and Probab. Lett. 50 (2000) 13). Under no...

We study the problems of super-replication and utility maximization from terminal wealth in a semimartingale model with countably many assets. After introducing a suitable definition of admissible strategy, we characterize superreplicable contingent claims in terms of martingale measures....

In this paper we study mutual absolute continuity, finiteness of relative entropy and the possibility of their equivalence for probability measures on C([0,[infinity]);Rd) induced by diffusion processes. We also determine explicit events which distinguish between two mutually singular measures...

We show that a wide class of stochastic processes on define currents for which we study the Sobolev regularity. This problem is associated to the pathwise definition of stochastic integrals.

For a strongly subcritical branching process (Zn)n[greater-or-equal, slanted]0 in random environment the non-extinction probability at generation n decays at the same exponential rate as the expected generation size and given non-extinction at n the conditional distribution of Zn has a weak...

We deal with backward stochastic differential equations with two reflecting barriers and a continuous coefficient which is, first, linear growth in (y,z) and then quadratic growth with respect to z. In both cases we show the existence of a maximal solution.

We consider a two-type stochastic competition model on the integer lattice . The model describes the space evolution of two "species" competing for territory along their boundaries. Each site of the space may contain only one representative (also referred to as a particle) of either type. The...

We analyze the lifetime consumption-portfolio problem in a competitive securities market with continuous price dynamics, possibly nontradeable income, and convex trading constraints. We define a class of "translation-invariant" recursive preferences, which includes additive exponential utility,...