Motivated by recent studies in financial mathematics and other areas, we investigate the exponential functional of a Lévy process X(t),t[greater-or-equal, slanted]0. In particular, we investigate its tail asymptotics. We show that, depending on the right tail of X(1), the tail behavior of Z is...

This paper deals with the solution u to the parabolic Anderson equation [not partial differential]u/[not partial differential]t=[kappa][Delta]u+[xi]u on the lattice . We consider the case where the potential [xi] is time-dependent and has the form [xi](t,x)=[delta]0(x-Yt) with Yt being a simple...

This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random fragmentation processes.

We aim to establish the existence and uniqueness of weak solutions to a suitable class of non-degenerate deterministic FBSDEs with a one-dimensional backward component. The classical Lipschitz framework is partially weakened: the diffusion matrix and the final condition are assumed to be space...

In this paper, we consider the renewal risk process with stochastic interest. For this risk process, we derive exact expressions and integral equations for the Gerber-Shiu expected discounted penalty function and the ultimate ruin probability. When the interest is received at a constant rate and...

Let (Xn) be a strictly stationary random sequence and Mn=max{X1,...,Xn}. Suppose that some of the random variables X1,X2,... can be observed and denote by the maximum of observed random variables from the set {X1,...,Xn}. We determine the limiting distribution of random vector under some...

We give functional limit theorems for the fluctuations of the rescaled occupation time process of a critical branching particle system in with symmetric [alpha]-stable motion in the cases of critical and large dimensions, d=2[alpha] and d2[alpha]. In a previous paper [T. Bojdecki, L.G....

Consider a data network model in which sources begin to transmit at renewal time points {Sn}. Transmissions proceed for random durations of time {Tn} and transmissions are assumed to proceed at fixed rate unity. We study M(t), the number of active sources at time t, a process we term the...

Backward stochastic Volterra integral equations (BSVIEs, for short) are introduced. The existence and uniqueness of adapted solutions are established. A duality principle between linear BSVIEs and (forward) stochastic Volterra integral equations is obtained. As applications of the duality...

It is shown that if a sequence of open n-sets Dk increases to an open n-set D then reflected stable processes in Dk converge weakly to the reflected stable process in D for every starting point x in D. The same result holds for censored [alpha]-stable processes for every x in D if D and Dk...