Fonctionnelles browniennes généralisées intégrale de Feynman
Fonctions aléatoires d'intervalle, IV
Forme de Dirichlet sur l'espace canonique de Poisson et applications aux équations différentielles stochastiques
Formule de Cauchy relative à certains lacets browniens
Formule de composition pour une classe d'opérateurs
Formule de Ito pour des processus non continus à valeurs dans des espaces de Banach
Formule de Taylor stochastique et développement asymptotique d'intégrales de Feynman
Formule d'Itô généralisée pour le mouvement brownien linéaire, d'après Föllmer Protter, Shiryaev
Formules de changement de variables
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