Lp-solutions of the stochastic transport equation

Stationary Solutions of the Stochastic Differential Equation

For a given bivariate Lévy process (Ut, Lt)t≥0, necessary and sufficient conditions for the existence of a strictly stationary solution of the stochastic differential equation dVt = Vt− dUt + dLt are obtained. Neither strict positivity of the stochastic exponential of U nor independence of V0 and (U,L) are assumed and noncausal solutions may appear. The form of the stationary solution is determ...

THE REVIEW OF ALMOST PERIODIC SOLUTIONS TO A STOCHASTIC DIERENTIAL EQUATION

This paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable Hilbert space. Themain technique is based upon an appropriate composition theorem combined with the Banachcontraction mapping principle and an analytic semigroup of linear operators.  

Deterministic and stochastic solutions of the Boltzmann equation for charge transport in graphene on substrates

A physically accurate model for charge transport in graphene is given by a semiclassical Boltzmann equation whose scattering terms have been deeply analyzed in the last decade. Due to the computational difficulties, the most part of the available solutions have been obtained with direct Monte Carlo simulations. The aim of this work is to simulate a monolayer graphene on a substrate, as, for ins...

Random Periodic Solutions of Stochastic Burgers Equation

The dynamics of randomly forced Burgers and Euler-Lagrange equations in S 1 × R d−1 in the case when there is only one one-sided minimizer in a compact subset of S 1 × R d−1 is studied. The existence of random invariant periodic minimizer orbits and periodicity of the stationary solution of the stochastic Burgers equations are obtained.

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION