We consider an interacting particle Markov process for Darwinian evolution in an asexual population with non-constant population size, involving a linear birth rate, a density-dependent logistic death rate, and a probability [mu] of mutation at each birth event. We introduce a renormalization...

We prove a duality theorem for the stochastic optimal control problem with a convex cost function and show that the minimizer satisfies a class of forward-backward stochastic differential equations. As an application, we give an approach, from the duality theorem, to h-path processes for...

We study the regularity of the viscosity solution of a quasilinear parabolic partial differential equation with Lipschitz coefficients by using its connection with a forward backward stochastic differential equation (in short FBSDE) and we give a probabilistic representation of the generalized...

Motivated by asymptotic problems in the theory of empirical processes, and specifically by tests of independence, we study the law of quadratic functionals of the (weighted) Brownian sheet and of the bivariate Brownian bridge on [0,1]2. In particular: (i) we use Fubini-type techniques to...

We consider an insurance company in the case when the premium rate is a bounded non-negative random function ct and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return a and volatility [sigma]0. If...

In a recent paper Pittet and Saloff-Coste established the lower bound , n=1,2,... for the large times asymptotic behaviours of the probabilities p2n(e,e) of return to the origin at even times 2n, for random walks associated with finite symmetric generating sets of solvable groups of finite...

We present a new version of the Central Limit Theorem for multivariate martingales.

Affine processes are distinguished by their rich structural properties, which makes them favorite when it comes to computations in financial applications of all kind. This fact has been explored and illustrated for the time-homogeneous case in a recent paper by Duffie, Filipovic and...

We consider asymptotic behavior of partial sums and sample covariances for linear processes whose innovations are dependent. Central limit theorems and invariance principles are established under fairly mild conditions. Our results go beyond earlier ones by allowing a quite wide class of...

We characterize, by means of an integral test, the upper and lower classes associated with the law of the iterated logarithm for subsequences. We also prove strong laws for the frequency of indices in connection with the lower class.