A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains.
A Uniform Law of the Iterated Logarithm for Brownian Motion on Compact Riemannian Manifolds.
A vanishing discount limit theorem for controlled Markov chains
A weak quasi-Lindelöf property and quasi-fine supports of measures.
A weighted empirical interpolation method: a priori convergence analysis and applications
We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667–672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis...
A zero-one law for integral functionals of the Bessel process
Abel transform and integrals of Bessel local times
About increments of additive functionals of diffusion processes.
About projections of logarithmic Sobolev inequalities
Absolute continuity of Markov processes
Accurate calculations of Stationary Distributions and Mean First Passage Times in Markov Renewal Processes and Markov Chains
This article describes an accurate procedure for computing the mean first passage times of a finite irreducible Markov chain and a Markov renewal process. The method is a refinement to the Kohlas, Zeit fur Oper Res, 30, 197–207, (1986) procedure. The technique is numerically stable in that it doesn’t involve subtractions. Algebraic expressions for the special cases of one, two, three and four states are derived.Aconsequence of the procedure is that the stationary distribution of the embedded Markov...
Adaptive control for discrete-time Markov processes with unbounded costs: Discounted criterion
We study the adaptive control problem for discrete-time Markov control processes with Borel state and action spaces and possibly unbounded one-stage costs. The processes are given by recurrent equations with i.i.d. -valued random vectors whose density is unknown. Assuming observability of we propose the procedure of statistical estimation of that allows us to prove discounted asymptotic optimality of two types of adaptive policies used early for the processes with bounded costs.
Adaptive dynamics in logistic branching populations
The biological theory of adaptive dynamics proposes a description of the long-time evolution of an asexual population, based on the assumptions of large population, rare mutations and small mutation steps. Under these assumptions, the evolution of a quantitative dominant trait in an isolated population is described by a deterministic differential equation called 'canonical equation of adaptive dynamics'. In this work, in order to include the effect of genetic drift in this model, we consider instead...
Adaptive wavelet estimation of the diffusion coefficient under additive error measurements
We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular in high frequency financial data modelling, however mainly from a parametric and semiparametric point of view. This paper addresses the nonparametric estimation of the path of the (possibly stochastic) diffusion coefficient in a relatively general setting. By...
Addendum : “A semi-markovian model for the brownian motion”
Addendum to the article “On ballistic diffusions in random environment”
Addendum to the paper : “On certain probabilities equivalent to Wiener measure”
Adding constraints to BSDEs with jumps: an alternative to multidimensional reflections
This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a minimal solution for these so-called constrained BSDEs with jumps via a penalization procedure. This new type of BSDE offers a nice and practical unifying framework to the notions of constrained BSDEs presented in [S. Peng and M. Xu, Preprint. (2007)] and BSDEs...
Additive functionals and excursions of Kuznetsov processes.
Additive functionals of Markov processes and stochastic systems
Intuitively, an additive functional of a stochastic process gives a method to measure time taking into account the development of the process. We associate with any set of states the mathematical expectation of time belongs to . In this way, we establish to one-to-one correspondence between all the normal additive functionals of a Markov process and all the -finite measures on the state space which charge no inaccessible set. This is proved under the condition that transition probabilities...