We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [17]. provide several criteria for existence and uniqueness of solutions which go beyond classical globally Lipschitz setting. In particular we show well-posedness equation, as well almost sure convergence associated particle ...

The Mel-frequency cepstral coefficients (MFCC) are most widely used and successful features for speech recognition. But, their performance degrades in presence of additive noise. In this paper, we propose a noise compensation method for Mel filter bank energies and so MFCC features. This compensation method includes two steps: Mel sub-band spectral subtraction and then compression of Mel-Sub-ba...

This paper provides a simplified proof for the existence of nested lattice codebooks allowing to achieve the capacity of the additive white Gaussian noise channel, as well as the optimal rate-distortion trade-off for a Gaussian source. The proof is self-contained and relies only on basic probabilistic and geometrical arguments. An ensemble of nested lattices that is different, and more elementa...

This paper investigates a dual-tone MFSK signalling technique for a frequency-hopped spread-spectrum communication system. It allows for multiple access communications with less transmission bandwidth and thus greater number of users than conventional MFSK. Both uncoded and coded dual-tone MFSK systems are considered in multiple access interference and additive white Gaussian noise with and wit...

The existence of random attractors for a large class of stochastic partial differential equations (SPDE) driven by general additive noise is established. The main results are applied to various types of SPDE, as e.g. stochastic reaction-diffusion equations, the stochastic p-Laplace equation and stochastic porous media equations. Besides classical Brownian motion, we also include space-time frac...

This contribution analyzes non-linear signal distortion in optical OFDM transmission channels. A “weakly non-linear” system approach is used, which treats non-linear signal distortion as additive noise. We review a technique for the separation of observed noise variances into several contributions. Furthermore scenarios are identified for which the compensation of non-linear signal distortion i...

A method of fuzzy likelihood-ratio hypothesis testing is applied to binary signal integration. Imprecise parameters of the distribution under each hypothesis are modeled as fuzzy numbers. The false alarm rate and detection rate are therefore also imprecise. The effects of parameter imprecision on integration performance are examined using an example; the method is applied to envelope detection ...

A Useful properties of the Moreau envelope and proximal map 14 A.1 Relation between proximal map and Moreau envelope . . . . . . . . . . . . . . . . 14 A.2 Relation between proximal map and derivative . . . . . . . . . . . . . . . . . . . . 15 A.3 Inverse of the Moreau envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 A.4 Moreau envelope for additive noise model . . . . . . . ...

We review some results concerning the apparition of finite time singularities in nonlinear Schrödinger equations with a Gaussian additive noise which is white in time and correlated in space. We then extend the results to the case where the noise is real valued, which is the case in some physical situations.