In recent years, infinite-dimensional methods have been introduced for the Gaussian channels estimation. The aim of this paper is to study the application of similar methods to Poisson channels. In particular we compute the Bayesian estimator of a Po
isson channel using the likelihood ratio and the discrete Malliavin gradient. This algorithm is suitable for numerical implementation via the Monte-Carlo scheme. As an application we provide an new proof of the formula obtained recently by Guo, Shamai and Verduu relating some derivatives of the input-output mutual information of a time-continuous Poisson channel and the conditional mean estimator of the input. These results are then extended to mixed Gaussian-Poisson channels.
In this paper we state and prove a central limit theorem for the finite-dimensional laws of the quadratic variations process of certain fractional Brownian sheets. The main tool of this article is a method developed by Nourdin and Nualart based on the Malliavin calculus.
In this paper we give a central limit theorem for the weighted quadratic variations process of a two-parameter Brownian motion. As an application, we show that the discretized quadratic variations $sum_{i=1}^{[n s]} sum_{j=1}^{[n t]} | Delta_{i,j} Y
|^2$ of a two-parameter diffusion $Y=(Y_{(s,t)})_{(s,t)in[0,1]^2}$ observed on a regular grid $G_n$ is an asymptotically normal estimator of the quadratic variation of $Y$ as $n$ goes to infinity.
