Abstract. A Boussinesq model for the Bénard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic Navier-Stokes equations and the transport equation for temperature. Large deviations are proved, using a weak convergence approach based on a variational representation of functionals of infinite dimensional...

Abstract. In this paper, we study the regularities of solutions of nonlinear stochastic partial differential equations in the framework of Hilbert scales. Then we apply our general result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau’s equations on the real line, stochastic 2D Navier-Stokes equations in the whole space and a stochastic tamed 3D Navier-Stokes ...

Existence and uniqueness for semilinear stochastic evolution equations with additive noise by means of finite-dimensional Galerkin approximations is established and the convergence rate of the Galerkin approximations to the solution of the stochastic evolution equation is estimated. These abstract results are applied to several examples of stochastic partial differential equations (SPDEs) of ev...

In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...

Semilinear stochastic evolution equations with multiplicative L'evy noise are considered‎. ‎The drift term is assumed to be monotone nonlinear and with linear growth‎. ‎Unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎As corollaries of ...

We have investigated the asset pricing problem in a general equilibrium in an economy with two states. Based on the assumption of a CRRA utility function, we have derived a partial differential equation satisfied by the representative agent’s cost function. In the case when the representative agent doesn’t have intermediate consumption, we have found an explicit solution of the cost function. A...

Streamwise velocity fluctuations in the inner-region of wall-bounded turbulent flows can be predicted by the model of Marusic, Mathis & Hutchins (2010). Only a single large-scale velocity signal from an outer position in the logarithmic region is needed for the model, and all other parameters are determined from a once-off calibration experiment. Here we elucidate part of the model by investiga...

Inbreeding avoidance and asymmetric competition over resources have both been identified as factors favouring the evolution of sex-biased dispersal. It has also been recognized that sex-specific costs of dispersal would select for sex-biased dispersal, but there is little quantitative information on this aspect. In this paper we explore (i) the quantitative relationship between cost-asymmetry a...

The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results.