On a high-dimensional nonlinear stochastic partial differential equation

In this paper we investigate a nonlinear stochastic partial differential equation (spde in short) perturbed by a space-correlated Gaussian noise in arbitrary dimension $d\geq1$, with a non-Lipschitz coefficient noisy term. The equation studied coincides in one dimension with the stochastic Burgers equation. Existence of a weak solution is established through an approximation procedure

Density estimates on a parabolic spde

We consider a general class of parabolic spde's [formula] with (t, x) [member of] [0, T]×[0, 1] and [epsilon]Wt,x, [epsilon] > 0, a perturbed Gaussian space-time white noise. For (t, x) [member of] (0, T]×(0, 1) we prove the called Davies and Varadhan-Léandre estimates of the density p[epsilon]t,x of the solution u[epsilon]t,x

Large deviations for a fractional stochastic heat equation in spatial dimension Rd\mathbb{R}^d driven by a spatially correlated noise

In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random influence which is a Gaussian noise, white in time and correlated in space. The differential operator is a fractional derivative operator. We prove a large deviations principle for our equation, using a weak convergence approach based on a variational representation of functionals of infinite-dimensional Brownian motion. This approach reduces the proof of LDP to establishing basic qualitative properties for controlled analogues of the original stochastic system.Comment: This paper has been accepted for publication in Stochastics & Dynamics. This reprint differs from the original in pagination and typographic detail. arXiv admin note: text overlap with arXiv:1309.1935 by other author

Adaptive Video Streaming Using TCP Factors Control with User Parameters

AbstractMedia streaming over TCP has become increasingly popular because TCP's congestion control provides remarkable stability to the Internet. Streaming over TCP requires adapting to bandwidth availability and other network parameters in order to have a good users satisfaction. Nowadays the streaming video can be projected on different kind of terminal as tablet, smart phones, laptop.etc. Each device has its own characteristics and parameters which must be taken into consideration on the video streaming adaptation process. In this paper, we propose an adaptive video streaming solution to improve the quality of experience (QoE) of the users by adapting TCP parameters to the user parameters on mobile networks. We validate the models using the ns2 simulator