A new sufficient condition for the existence of a stationary causal solution of an equation is provided. This condition allows us to consider coefficients with power-law decay, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved.

Consider the high-order heat-type equation [not partial differential]u/[not partial differential]t=(-1)1+N/2[not partial differential]Nu/[not partial differential]xN for an even integer N2, and introduce the related Markov pseudo-process (X(t))t[greater-or-equal, slanted]0. Let us define the...

We introduce a sequence of stopping times that allow us to study an analogue of a life-cycle decomposition for a continuous time Markov process, which is an extension of the well-known splitting technique of Nummelin to the continuous time case. As a consequence, we are able to give...

We derive some results on contrarian and one-sided strategies of Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk [G. Shafer and V. Vovk. Probability and Finance -- It's Only a Game!, Wiley, New York, 2001]. In particular, as regards the rate...

We study a discrete-time approximation for solutions of systems of decoupled Forward-Backward Stochastic Differential Equations (FBSDEs) with jumps. Assuming that the coefficients are Lipschitz-continuous, we prove the convergence of the scheme when the number of time steps n goes to infinity....

In this paper we will examine the derivative of intersection local time of Brownian motion and symmetric stable processes in . These processes do  not exist when defined in the canonical way. The purpose of this paper is to exhibit the correct rate for renormalization of these processes.

We consider statistical mechanics models of continuous height effective interfaces in the presence of a delta pinning of strength [epsilon] at height zero. There is a detailed mathematical understanding of the depinning transition in two dimensions without disorder. Then the variance of the...

A terminal perturbation method is introduced to study the backward approach to continuous time mean-variance portfolio selection with bankruptcy prohibition in a complete market model. Using Ekeland's variational principle, we obtain a necessary condition, i.e. the stochastic maximum principle,...

We present a class of Lévy processes for modelling financial market fluctuations: bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated Lévy processes. We treat exponential Lévy stock models with an...

Given a finite collection of continuous semimartingales, we derive a semimartingale decomposition of the corresponding ranked (order-statistics) processes. We apply the decomposition to extend the theory of equity portfolios generated by ranked market weights to the case where the stock values...