A simple proof of the support theorem for diffusion processes
A stochastic inventory model with stock dependent demand items.
A stochastic model of symbiosis
We consider a system of stochastic differential equations which models the dynamics of two populations living in symbiosis. We prove the existence, uniqueness and positivity of solutions. We analyse the long-time behaviour of both trajectories and distributions of solutions. We give a biological interpretation of the model.
A stochastic scheme for constructing solutions of the Schrödinger equations
A stochastic symbiosis model with degenerate diffusion process
We present a model of symbiosis given by a system of stochastic differential equations. We consider a situation when the same factor influences both populations or only one population is stochastically perturbed. We analyse the long-time behaviour of the solutions and prove the asymptoptic stability of the system.
A trivariate law for certain processes related to perturbed brownian motions
A unified approach to several inequalities for gaussian and diffusion measures
About projections of logarithmic Sobolev inequalities
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 to the article “On ballistic diffusions in random environment”
Affine Dunkl processes of type
We introduce the analogue of Dunkl processes in the case of an affine root system of type . The construction of the affine Dunkl process is achieved by a skew-product decomposition by means of its radial part and a jump process on the affine Weyl group, where the radial part of the affine Dunkl process is given by a Gaussian process on the ultraspherical hypergroup . We prove that the affine Dunkl process is a càdlàg Markov process as well as a local martingale, study its jumps, and give a martingale...
Almost sure path properties of branching diffusion processes
An application of the Bakry-Émery criterion to infinite dimensional diffusions
An approximation scheme for the optimal control of diffusion processes
An explicit representation of the extended Skorokhod map with two time-dependent boundaries.
An extension of Krein's inverse spectral theorem to strings with nonreflecting left boundaries
An extension of the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps.
An interacting particles process for Burgers equation on the circle.
Anwendungen der Theorie der optimalen Regelungnichtabbrechender Diffusionsprozesse
Appendice : «Un résultat de D. Williams»