Équations différentielles stochastiques linéaires : la méthode de variation des constantes
Équations différentielles stochastiques lipschitziennes : étude de la stabilité
Équations différentielles stochastiques multivoques unidimensionnelles
Equations in differentials in the algebra of generalized stochastic processes
We consider an ordinary or stochastic nonlinear equation with generalized coefficients as an equation in differentials in the algebra of new generalized functions in the sense of [8]. Consequently, the solution of such an equation is a new generalized function. We formulate conditions under which the solution of a given equation in the algebra of new generalized functions is associated with an ordinary function or process. Moreover the class of all possible associated functions and processes is...
Estimation de grandes déviations pour les processus de diffusion à paramètre multidimensionnel
Estudio del carácter markoviano fuerte y regularidades de la solución de ecuaciones integrales estocásticas Ito generalizadas.
El objetivo de este trabajo es un estudio sobre los caracteres felleriano y markoviano fuerte y las propiedades de regularidad del proceso solución de una ecuación integral estocástica generalizada (tipo Ito), pero generalizada en el sentido de considerar una formulación en términos de procesos operador-valuados. Esta formulación generaliza simultánea e independientemente las integrales de Cabaña y Daletsky.
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.