Let $X$ be the fractional Brownian motion of any Hurst index $H\in (0,1)$ (resp. a semimartingale) and set $\alpha=H$ (resp. $\alpha=\frac{1}{2}$). If $Y$ is a continuous process and if $m$ is a positive integer, we study the existence of the…

The higher-order heat-type equation $ \partial u/\partial t=\pm\partial^{n} u/ \partial x^{n} $ has been investigated by many authors. With this equation is associated a pseudo-process $(X_t)_{t\ge 0}$ which is governed by a signed measure. In the even-order case, Krylov (1960)…

We consider the critical spread-out contact process in $Z^d$ with $d\geq1$, whose infection range is denoted by $L\geq1$. The two-point function $\tau_t(x)$ is the probability that $x\in Z^d$ is infected at time $t$ by the infected individual located at the…

This paper concerns the issue of obtaining the large deviation principle for solutions of stochastic equations with possibly degenerate coefficients. Specifically, we explore the potential of the methodology that consists in establishing exponential tightness and identifying the action functional via…

Let $X$ be a linear diffusion and $f$ a non-negative, Borel measurable function. We are interested in finding conditions on $X$ and $f$ which imply that the perpetual integral functional $$ I^X_\infty(f):=\int_0^\infty f(X_t) dt $$ is identical in law with…

We consider a parallel server queueing system consisting of a bank of buffers for holding incoming jobs and a bank of flexible servers for processing these jobs. Incoming jobs are classified into one of several different classes (or buffers). Jobs…

We study dynamic monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a dynamic risk measure time-consistent if it assigns to a process of…