Calls arrive in a Poisson stream on a symmetric network constituted of N links of capacity C. Each call requires one channel on each of L distinct links chosen uniformly at random; if none of these links is full, the call is accepted and holds one channel per link for an exponential duration,...

We study a stochastic optimization problem under constraints in a general framework including financial models with constrained portfolios, labor income and large investor models and reinsurance models. We also impose American-type constraint on the state space process. General objective...

In this paper we prove the existence of the quadratic covariation [([not partial differential]F/[not partial differential]xk)(X), Xk] for all 1[less-than-or-equals, slant]k[less-than-or-equals, slant]d, where F belongs locally to the Sobolev space for some pd and X is a d-dimensional smooth...

We study existence and continuity of self-intersection local time of any order of Gaussian processes. In particular, we give results for Wiener and Ornstein-Uhlenbeck processes. We study processes associated with several classes of covariances, which arise in examples mainly as fluctuation...

In this paper, inspired by the idea of Metropolis algorithm, a new sample adaptive simulated annealing algorithm is constructed on finite state space. This new algorithm can be considered as a substitute of the annealing of iterative stochastic schemes. The convergence of the algorithm is shown.

We fit a class of semiparametric models to a nonstationary process. This class is parametrized by a mean function [mu](·) and a p-dimensional function [theta](·)=([theta](1)(·),...,[theta](p)(·))' that parametrizes the time-varying spectral density f[theta](·)([lambda]). Whereas...

For stochastic differential equations reflecting on the boundary of a general convex domain the convergence in Lp and almost surely for recursive projection and discrete penalization schemes are considered. Earlier results by Liu (Ph.D. Thesis, Purdue University), Pettersson (Stochastic Process....

An averaging principle is proved for diffusion processes of type (X[var epsilon](t),Y[var epsilon](t)) with null-recurrent fast component X[var epsilon](t). In contrast with positive recurrent setting, the slow component Y[var epsilon](t) alone cannot be approximated by diffusion processes....

We present an introduction to mathematical Finance Theory for mathematicians. The approach is to start with an abstract setting and then introduce hypotheses as needed to develop the theory. We present the basics of European call and put options, and we show the connection between American put...

We study in this paper anticipative transformations on the Poisson space in the framework introduced by Picard (Ann. Inst. Henri Poincare 32 (4) (1996a) 509). Those are stochastic transformations that add particles to an initial condition or remove particles to it; they may be seen as a...