It is shown that value functions for controlled degenerate diffusion processes can be approximated with error of order $h^{1/3}$ by using policies which are constant on intervals $[kh^{2},(k+1)h^{2})$.

Genetic models incorporating resampling and migration are now fairly well-understood. Problems arise in the analysis, if both selection and mutation are incorporated. This paper addresses some aspects of this problem, in particular the analysis of the long-time behaviour before the…

In this paper we investigate stopped partial sums for weak dependent sequences. In particular, the results are used to obtain new maximal inequalities for strongly mixing sequences and related almost sure results.

We establish a large deviations type evaluation for the family of integral functionals.

Let $G$ be a finite group. Choose a set $S$ of size $k$ uniformly from $G$ and consider a lazy random walk on the corresponding Cayley graph. We show that for almost all choices of $S$ given $k = 2a\,…

We present an upper bound on the mixing rate of the equilibrium state of a dynamical system defined by the one-sided shift and a non Hölder potential of summable variations. The bound follows from an estimation of the relaxation speed…

Recently, Naiman and Wynn introduced the concept of an abstract tube in order to obtain improved inclusion-exclusion identities and inequalities that involve much fewer terms than their classical counterparts. In this paper, we introduce a particular class of abstract tubes…

We extend the definition of Walsh's martingale measure stochastic integral so as to be able to solve stochastic partial differential equations whose Green's function is not a function but a Schwartz distribution. This is the case for the wave equation…

We study the weak convergence for the row sums of a general triangular array of empirical processes indexed by a manageable class of functions converging to an arbitrary limit. As particular cases, we consider random series processes and normalized sums…

We prove moderate deviations principles for unbounded additive functionals of the form $S_n = \sum_{j=1}^{n} g(X^{(p)}_{j-1})$, where $(X_n)_{n\in N}$ is a stable $R^d$-valued functional autoregressive model of order $p$ with white noise and stationary distribution $\mu$, and $g$ is an…