In this paper we investigate the cluster behavior of linearly interacting Brownian motions indexed by . We show that (on a logarithmic scale) the block average process converges in path space to Brownian motion.

This paper offers a way to construct a locally optimal stationary approximation for a non-stationary Gaussian process. In cases where this construction leads to a unique stationary approximation we call it a stationary tangent. This is the case with Gaussian processes governed by smooth...

We study the problem of minimal initial capital needed in order to hedge a European contingent claim without risk. The financial market presents incompleteness arising from two sources: stochastic volatility and portfolio constraints described by a closed convex set. In contrast with previous...

We give necessary and sufficient conditions in order that exponentials of additive functionals of Markov processes have finite expectations. Furthermore, we obtain sharp estimates for these expectations. More precisely, we investigate both the Stieltjes exponential and the ordinary exponential...

A simple graphical argument described in a previous paper is used to show that the zero-modified geometric form of the population-size distribution of a time-inhomogeneous birth-and-death model is maintained when the death rates of individuals depend on their ages and times of birth. An explicit...

In this paper, we will present a method to construct a spatially inhomogeneous process on the p-adic number field. Secondly, we will modify the definition of the derivative of real-valued function on the field, hinted by the Fourier transformation. As a result, we can introduce a class of...

Solutions to stochastic differential equations depends on the method of approximation. In this paper we give a very simple demonstration that ordinary differential equations, too, exhibit this kind of behavior when the coefficients are measure-valued distributions. We then proceed to show that...

We establish a central limit theorem for the logarithm of the characteristic polynomial of a random permutation matrix. We relate this result to a central limit theorem of Wieand for the counting function for the eigenvalues lying in some interval on the unit circle.

We consider a one-dimensional totally asymmetric nearest-neighbor zero-range process with site-dependent jump-rates - an environment. For each environment p we prove that the set of all invariant measures is the convex hull of a set of product measures with geometric marginals. As a consequence...

We consider a non-local operator L associated to a Markov process with jumps, we stop this process when it quits a domain D, and we study the Cj smoothness on D of the functions which are harmonic for the stopped process. A previous work was devoted to the existence of a C[infinity] transition...