Formules de dualité sur l'espace de Poisson
Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients
We consider a system of fully coupled forward-backward stochastic differential equations. First we generalize the results of Pardoux-Tang [7] concerning the regularity of the solutions with respect to initial conditions. Then, we prove that in some particular cases this system leads to a probabilistic representation of solutions of a second-order PDE whose second order coefficients depend on the gradient of the solution. We then give some examples in dimension 1 and dimension 2 for which the assumptions...
Fractional differential equations driven by Lévy noise.
Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations
MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf GorenfloThere is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called Fokker-Planck equations, also called Kolmogorov equations. The Brownian motion plays the role of the basic driving process for SDEs. This paper provides fractional generalizations of the triple relationship between the driving process, corresponding...
Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series
We introduce a fractional Langevin equation with α-stable noise and show that its solution is the stationary α-stable Ornstein-Uhlenbeck-type process recently studied by Taqqu and Wolpert. We examine the asymptotic dependence structure of via the measure of its codependence r(θ₁,θ₂,t). We prove that is not a long-memory process in the sense of r(θ₁,θ₂,t). However, we find two natural continuous-time analogues of fractional ARIMA time series with long memory in the framework of the Langevin...
Fractional Ornstein-Uhlenbeck processes.
Fredholm random operators and random subspaces in Banach spaces
From an example of Lévy's
From power pure point to continuous spectrum in disordered systems
From random telegraph to Gaussian stochastic noises: decoherence and spectral diffusion in a semiconductor quantum dot.
From Tanaka's formula to Ito's formula : distributions, tensor products and local times
Fubini's theorem for double Wiener integrals and the variance of the brownian path
Full cooperation applied to environmental improvements
We analyse the case of certificates of environmental improvements and full cooperation of two identical agents. We model pollution levels as geometric Brownian motions with quadratic costs of improvements. Our main result is the construction of the optimal improvements strategy in the case of separate actions, collusive actions and fusion. In certain range of the model parameters, the fusion solution generates lower pollution levels than separate and collusive actions.
Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise
We consider an initial and Dirichlet boundary value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. Discretizing the space-time white noise a modelling error is introduced and a regularized fourth-order linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized problem are constructed by using, for discretization in space, a Galerkin finite element method...
Functional integro-differential stochastic evolution equations in Hilbert space.
Functionals on transient stochastic processes with independent increments
The paper is devoted to the study of integral functionals for a wide class of functions f and transient stochastic processes X(t,ω) with stationary and independent increments. In particular, for nonnegative processes a random analogue of the Tauberian theorem is obtained.
Fundamental solutions to Kolmogorov equations via reduction to canonical form.
Fundamental theorems for linear measure differential equations.
Galerkin approximation and the strong solution of the Navier-Stokes equation.
Gaussian approximations of multiple integrals.