Équations différentielles stochastiques lipschitziennes
Espaces de Fock pour les processus de Wiener et de Poisson
Euler's Approximations of Solutions of Reflecting SDEs with Discontinuous Coefficients
Let D be either a convex domain in or a domain satisfying the conditions (A) and (B) considered by Lions and Sznitman (1984) and Saisho (1987). We investigate convergence in law as well as in for the Euler and Euler-Peano schemes for stochastic differential equations in D with normal reflection at the boundary. The coefficients are measurable, continuous almost everywhere with respect to the Lebesgue measure, and the diffusion coefficient may degenerate on some subsets of the domain.
Euler's Approximations of Weak Solutions of Reflecting SDEs with Discontinuous Coefficients
We study convergence in law for the Euler and Euler-Peano schemes for stochastic differential equations reflecting on the boundary of a general convex domain. We assume that the coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. The proofs are based on new estimates of Krylov's type for the approximations considered.
Exponential asymptotic stability of linear Itô-Volterra equations with damped stochastic perturbations.