Géométrie stochastique sans larmes, I
Geometry of stochastic delay differential equations.
Girsanov type formula for a Lie group valued brownian motion
Global asymptotic stability of solutions of cubic stochastic difference equations.
Global existence and controllability to a stochastic integro-differential equation.
Global geometry under isotropic Brownian flows.
Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase
In the present note, we review some recent results on the spectral statistics of random operators in the localized phase obtained in [12]. For a general class of random operators, we show that the family of the unfolded eigenvalues in the localization region considered jointly with the associated localization centers is asymptotically ergodic. This can be considered as a generalization of [10]. The benefit of the present approach is that one can vary the scaling of the unfolded eigenvalues covariantly...
Grandes déviations spatiales pour un système gradient stochastique infini-dimensionnel
Grossissement d'une filtration et retournement du temps d'une diffusion
Harmonic functions on loop groups
Heat kernel measure on central extension of current groups in any dimension.
Hedging in complete markets driven by normal martingales
This paper aims at a unified treatment of hedging in market models driven by martingales with deterministic bracket , including Brownian motion and the Poisson process as particular cases. Replicating hedging strategies for European, Asian and Lookback options are explicitly computed using either the Clark-Ocone formula or an extension of the delta hedging method, depending on which is most appropriate.
Hermite martingales
Hiding a constant drift
The following question is due to Marc Yor: Let B be a brownian motion and St=t+Bt. Can we define an -predictable process H such that the resulting stochastic integral (H⋅S) is a brownian motion (without drift) in its own filtration, i.e. an -brownian motion? In this paper we show that by dropping the requirement of -predictability of H we can give a positive answer to this question. In other words, we are able to show that there is a weak solution to Yor’s question. The original question, i.e.,...
Hilbert space valued generalized random processes. I.
Hilbert-valued anticipating stochastic differential equations
Hitting properties of a random string.
Hitting time of a corner for a reflected diffusion in the square
We discuss the long time behavior of a two-dimensional reflected diffusion in the unit square and investigate more specifically the hitting time of a neighborhood of the origin. We distinguish three different regimes depending on the sign of the correlation coefficient of the diffusion matrix at the point 0. For a positive correlation coefficient, the expectation of the hitting time is uniformly bounded as the neighborhood shrinks. For a negative one, the expectation explodes in a polynomial way...
Hochschild cohomology theories in white noise analysis.
Hölder norms and the support theorem for diffusions