We formalize and analyze the notions of stochastic monotonicity and realizable monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are...

In this paper, we study the initial value problem for a class of non-linear stochastic equations of Burgers type of the following form [not partial differential]tu+q(x,D)u+[not partial differential]xf(t,x,u)=h1(t,x,u)+h2(t,x,u)Ft,x for , where q(x,D) is a pseudo-differential operator with...

We study a time-non-homogeneous Markov process which arose from free probability, and which also appeared in the study of stochastic processes with linear regressions and quadratic conditional variances. Our main result is the explicit expression for the generator of the (non-homogeneous)...

In this paper we consider the power utility maximization problem under partial information in a continuous semimartingale setting. Investors construct their strategies using the available information, which possibly may not even include the observation of the asset prices. Resorting to...

The long time asymptotics of the time spent on the positive side are discussed for one-dimensional diffusion processes in random environments. The limiting distributions under the log-log scale are obtained for the diffusion processes in the stable medium as well as for the Brox model. Similar...

We study the problem of optimally hedging exotic derivatives positions using a combination of dynamic trading strategies in underlying stocks and static positions in vanilla options when the performance is quantified by a convex risk measure. We establish conditions for the existence of an...

For self-avoiding walks on the d-dimensional cubic lattice defined with a positive bias in one of the coordinate directions, it is proved that the drift in the favored direction is strictly positive.

We introduce a class of models of semiflexible polymers. The latter are characterized by a strong rigidity, the correlation length associated with the gradient-gradient correlations, called the persistence length, being of the same order as the polymer length. We determine the macroscopic...

We establish that the image of a measure, which satisfies a certain energy condition, moving under a standard isotropic Brownian flow will, when properly scaled, have an asymptotically normal distribution under almost every realization of the flow. We derive the same result for an initial point...

We consider random walk with a nonzero bias to the right, on the infinite cluster in the following percolation model: take i.i.d. bond percolation with retention parameter p on the so-called infinite ladder, and condition on the event of having a bi-infinite path from -[infinity] to...