We propose a new approach to constructing weak numerical methods for finding solutions to stochastic systems with small noise. For these methods we prove an error estimate in terms of products hiεj (h is a time increment, ε is a small parameter). We derive various efficient weak schemes for systems with small noise and study the Talay–Tubaro expansion of their global error. An efficient approac...

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications-the backbone of the internet. At large signal-to-noi...

Using the path-integral technique we examine the mutual information for the communication channel modelled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications — the backbone of the Internet. At large signal-to-...

The generation of coherent dynamics due to noise in an activator-inhibitor system describing bistable neural dynamics is investigated. We show that coherence can be induced in deterministically asymmetric regimes via symmetry restoration by multiplicative noise, together with the action of additive noise which induces jumps between the two stable steady states. The phenomenon is thus doubly sto...

The aim of this paper is the rigorous derivation of a stochastic non-linear diffusion equation from a radiative transfer equation perturbed with a random noise. The proof of the convergence relies on a formal Hilbert expansion and the estimation of the remainder. The Hilbert expansion has to be done up to order 3 to overcome some difficulties caused by the random noise.

We present examples of equations arising in the theory mean field games that can be reduced to a system smaller dimensions. Such come up certain applications, and they used as modeling tools numerically approximate more complicated problems. General conditions bring about reduction phenomena are presented both finite infinite state-space cases. also compare solutions with noise their versions s...