On some fractional stochastic integrodifferential equations in Hilbert space.
On some limit theorems for solutions of stochastic differential equations
On some stability properties of stochastic differential equations of Itô's type
On stability for numerical approximations of stochastic ordinary differential equations.
On stochastic differential equations in a configuration space.
On stochastic differential equations with locally unbounded drift
We study the regularizing effect of the noise on differential equations with irregular coefficients. We present existence and uniqueness theorems for stochastic differential equations with locally unbounded drift.
On the approximate solutions of the Stratonovitch equation.
On the consistency of a least squares identification procedure
On the constructions of the skew Brownian motion.
On the control of the difference between two Brownian motions: a dynamic copula approach
We propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Brownian motion and its reflection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right...
On the control of the difference between two Brownian motions: an application to energy markets modeling
We derive a model based on the structure of dependence between a Brownian motion and its reflection according to a barrier. The structure of dependence presents two states of correlation: one of comonotonicity with a positive correlation and one of countermonotonicity with a negative correlation. This model of dependence between two Brownian motions B1 and B2 allows for the value of [...] to be higher than 1/2 when x is close to 0, which is not the case when the dependence is modeled by a constant...
On the convergence of generalized polynomial chaos expansions
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement...
On the convergence of generalized polynomial chaos expansions
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial...
On the estimation in a class of diffusion-type processes. Aplication for diffusion branching processes.
In this work a family of stochastic differential equations whose solutions are multidimensional diffusion-type (non necessarily markovian) processes is considered, and the estimation of a parametric vector θ which relates the coefficients is studied. The conditions for the existence of the likelihood function are proved and the estimator is obtained by continuously observing the process. An application for Diffusion Branching Processes is given. This problem has been studied in some special cases...
On the estimation of the diffusion coefficient for multi-dimensional diffusion processes
On the infinite time horizon linear-quadratic regulator problem under a fractional brownian perturbation
In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic gaussian regulator problem. For a completely observable controlled linear system driven by a fractional brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.
On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation
In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic Gaussian regulator problem. For a completely observable controlled linear system driven by a fractional Brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.
On the innovations conjecture of nonlinear filtering with dependent data.
On the limiting behavior of a harmonic oscillator with random external disturbance.
On the long-time behaviour of a class of parabolic SPDE’s : monotonicity methods and exchange of stability
In this article we prove new results concerning the structure and the stability properties of the global attractor associated with a class of nonlinear parabolic stochastic partial differential equations driven by a standard multidimensional brownian motion. We first use monotonicity methods to prove that the random fields either stabilize exponentially rapidly with probability one around one of the two equilibrium states, or that they set out to oscillate between them. In the first case we can...