Die Zurückführung einiger in der Wahrscheinlichkeitsrechnung und in der Statistik auftretenden Integrale auf andere allgemeine Integrale
Diffeomorphisms of the circle and the based stochastic loop space
Difference of general integral means.
Different approaches to stochastic parabolic differential equations
Differentation along algebras.
Différentiabilité des fonctions finement harmoniques.
Différentiabilité fine, différentiabilité stochastique, différentiabilité stochastique de fonctions finement harmoniques
Dans ce travail, nous définissons et étudions la notion de “différentiabilité stochastique” d’une fonction définie sur un ouvert fin d’une variété riemannienne de dimension finie. Nous démontrons ensuite qu’une fonction admettant une “suite d’approximation forte” est, quasi-partout, stochastiquement indéfiniment différentiable et nous appliquons ces résultats à une classe de fonctions finement harmoniques.
Différentiabilité fine et différentiabilité sur des compacts
Différentiabilité stochastique des fonctions finement harmoniques.
Differentiability of excessive functions of one-dimensional diffusions and the principle of smooth fit
The principle of smooth fit is probably the most used tool to find solutions to optimal stopping problems of one-dimensional diffusions. It is important, e.g., in financial mathematical applications to understand in which kind of models and problems smooth fit can fail. In this paper we connect-in case of one-dimensional diffusions-the validity of smooth fit and the differentiability of excessive functions. The basic tool to derive the results is the representation theory of excessive functions;...
Differentiability of multiplicative processes related to branching random walks
Differentiability of stochastic flow of reflected Brownian motions.
Differential equation approximations for Markov chains.
Differential equations driven by fractional Brownian motion.
A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.
Differential equations driven by gaussian signals
We consider multi-dimensional gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of Lévy area(s). gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful – yet conceptually simple – framework in which to analyze differential equations driven by gaussian signals in the rough paths sense.
Differential equations driven by rough signals.
This paper aims to provide a systematic approach to the treatment of differential equations of the typedyt = Σi fi(yt) dxti where the driving signal xt is a rough path. Such equations are very common and occur particularly frequently in probability where the driving signal might be a vector valued Brownian motion, semi-martingale or similar process.However, our approach is deterministic, is totally independent of probability and permits much rougher paths than the Brownian paths usually discussed....
Differential equations of stochastic processes which have derivative in quadratic mean
Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials: the discrete case.
Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. The continuous case.
Differential properties of measures on infinite dimensional spaces and the Malliavin calculus