Diffusions hypercontractives
Diffusions in random environment and ballistic behavior
Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized burgers' equations
Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized Burgers' equations
We prove existence and uniqueness for two classes of martingale problems involving a nonlinear but bounded drift coefficient. In the first class, this coefficient depends on the time t, the position x and the marginal of the solution at time t. In the second, it depends on t, x and p(t,x), the density of the time marginal w.r.t. Lebesgue measure. As far as the dependence on t and x is concerned, no continuity assumption is made. The results, first proved for the identity diffusion matrix,...
Diffusions with measurement errors. I. Local asymptotic normality
We consider a diffusion process which is observed at times for , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance . There is an unknown parameter within the diffusion coefficient, to be estimated. In this first paper the case when is indeed a gaussian martingale is examined: we can prove that the LAN property holds under quite weak smoothness assumptions, with an explicit limiting Fisher information. What is perhaps...
Diffusions with measurement errors. I. Local Asymptotic Normality
We consider a diffusion process X which is observed at times i/n for i = 0,1,...,n, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known variance pn. There is an unknown parameter within the diffusion coefficient, to be estimated. In this first paper the case when X is indeed a Gaussian martingale is examined: we can prove that the LAN property holds under quite weak smoothness assumptions, with an explicit limiting Fisher information....
Diffusions with measurement errors. II. Optimal estimators
We consider a diffusion process which is observed at times for , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance . There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process is a gaussian martingale, and we conjecture that they are also optimal in the general case.
Diffusions with measurement errors. II. Optimal estimators
We consider a diffusion process X which is observed at times i/n for i = 0,1,...,n, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known variance pn. There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process X is a Gaussian martingale, and we conjecture that they are also optimal in the general case.
Dirichlet forms, quasiregular functions and Brownian motion.
Discounted optimal stopping for maxima in diffusion models with finite horizon.
Discrete Models of Time-Fractional Diffusion in a Potential Well
Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.By generalization of Ehrenfest’s urn model, we obtain discrete approximations to spatially one-dimensional time-fractional diffusion processes with drift towards the origin. These discrete approximations can be interpreted (a) as difference schemes for the relevant time-fractional partial differential equation, (b) as random walk models. The relevant convergence questions as well as the behaviour for time tending to infinity...
Distributions of functionals of diffusions with jumps.
Dynamic programming for stochastic target problems and geometric flows
Dynamic scheduling of a parallel server system in heavy traffic with complete resource pooling: asymptotic optimality of a threshold policy.
Dynamical properties and characterization of gradient drift diffusions.
Dyson's Brownian motions, intertwining and interlacing.
Eigenvalues of the Laguerre process as non-colliding squared Bessel processes.
Energy and the law of the interated logarithm.
Équations différentielles stochastiques multivoques
Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere
We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering only solutions which are independent of the space variable. This simplification leads to a degenerate stochastic equation in the tangent bundle of the 2D sphere. Studying this equation, we prove existence and non-uniqueness of invariant probability measures for the original problem and obtain also results on attractivity towards an invariant measure. We also...