Anticipative calculus with respect to filtered Poisson processes
Anticipative direct transformations on the Poisson space
Appendice à l'exposé précédent : «Inégalités de semimartingales»
Appendice : «Un résultat de D. Williams»
Application du calcul de Malliavin aux équations différentielles stochastiques sur le plan
Application du théorème de Scorza Dragoni aux équations différentielles stochastiques
Applications du temps local aux équations différentielles stochastiques unidimensionnelles
Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance
We investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in insurance and finance in an attempt to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending on the strategy applied or the past values of the portfolio. In this setting, a managed investment portfolio serves simultaneously as the underlying security on which the liability/target...
Approximate controllability of neutral stochastic integrodifferential systems in Hilbert spaces.
Approximation and optimality necessary conditions in relaxed stochastic control problems.
Approximation at first and second order of -order integrals of the fractional Brownian motion and of certain semimartingales.
Approximation by time discretization of special stochastic evolution equations.
Approximation des trajectoires et temps local des diffusions
Approximation of attractors for multivalued random dynamical systems
Approximation of bivariate Markov chains by one-dimensional diffusion processes
The paper deals with several questions of the diffusion approximation. The goal of this paper is to create the general method of reducting the dimension of the model with the aid of the diffusion approximation. Especially, two dimensional random variables are approximated by one-dimensional diffusion process by replacing one of its coordinates by a certain characteristic, e.g. by its stationary expectation. The suggested method is used for several different systems. For instance, the method is applicable...
Approximation of finite-dimensional distributions for integrals driven by α-stable Lévy motion
We present a method of numerical approximation for stochastic integrals involving α-stable Lévy motion as an integrator. Constructions of approximate sums are based on the Poissonian series representation of such random measures. The main result gives an estimate of the rate of convergence of finite-dimensional distributions of finite sums approximating such stochastic integrals. Stochastic integrals driven by such measures are of interest in constructions of models for various problems arising...
Approximation of stochastic advection diffusion equations with stochastic alternating direction explicit methods
The numerical solutions of stochastic partial differential equations of Itô type with time white noise process, using stable stochastic explicit finite difference methods are considered in the paper. Basically, Stochastic Alternating Direction Explicit (SADE) finite difference schemes for solving stochastic time dependent advection-diffusion and diffusion equations are represented and the main properties of these stochastic numerical methods, e.g. stability, consistency and convergence are analyzed....
Approximation par des intégrales de Stieltjes-Lebesgue d’intégrales stochastiques relatives au mouvement brownien indexé par
Approximation par des intégrales de Stieltjes-Lebesgue d’intégrales stochastiques relatives au mouvement brownien indexé par
Approximation scheme for solutions of backward stochastic differential equations via the representation theorem
We are interested in the approximation and simulation of solutions for the backward stochastic differential equations. We suggest two approximation schemes, and we study the induced error.