We study the mixed formulation of the stochastic Hodge–Laplace problem defined on an n-dimensional domain D (n 1), with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three-dimensional case. We derive and analyse the moment equations, that is, the deterministic equations solved by the mth moment (m 1) of the unique stochastic solution o...

An extension of the deterministic variational multiscale (VMS) approach with algebraic subgrid scale (SGS) modeling is considered for developing stabilized finite element formulations for the stochastic advection and the incompressible stochastic Navier-Stokes equations. The stabilized formulations are numerically implemented using the spectral stochastic formulation of the finite element metho...

This paper is dedicated to the study of stochastic finite-time stability (SFTS) and control synthesis for a class of nonlinear Markovian jump stochastic systems with impulsive effects. By introducing a time-varying stochastic Lyapunov function with discontinuities at impulse times, an improved criterion for SFTS is derived in terms of linear matrix inequalities (LMIs). Based on the new SFTS cri...

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method...

We consider natural convection in flow saturated porous media with random porosity. The porosity is treated as a random field and a stochastic finite element method is developed. The stochastic projection method is considered for the solution of the high-dimensional stochastic Navier-Stokes equations since it leads to the uncoupling of the velocity and pressure degrees of freedom. Because of th...

A new class of non-Markovian models is introduced that results from the combination of stochastic automata networks and a very general class of stochastic processes namely rational arrival processes which are derived from matrix exponential distributions. It is shown that the modeling formalism allows a compact representation of complex models with large state spaces. The resulting stochastic p...

This paper describes the MQNA Markovian Queueing Networks Analyser, a software tool to model and obtain the stationary solution of a large class of Queueing Networks. MQNA can directly solve open and closed product-form queueing networks using classical algorithms. For finite capacity queueing models, MQNA generates Markovian description in the Stochastic Automata Networks (SAN) and Stochastic ...

A stochastic process ξ(t) = ξ(t,ω) (−∞ < t < ∞) with values in R is said to be stationary (in the strict sense) if for every finite sequence of numbers t1, . . . , tn the joint distribution of the random variables ξ(t1 + h), . . . , ξ(tn + h) is independent of h. If we replace the arbitrary number h by a multiple of a fixed number θ , h= kθ (k =±1,±2, . . . ), we get the definition of a periodi...

naturally occurred soil deposits inherit heterogeneity and anisotropy in their strength properties. the main purpose of this paper is to model the soil stratum with anisotropy consideration and spatially varying undrained shear strength by using random field theory coupled with finite difference numerical analysis to evaluate their effect on the bearing capacity of the shallow foundations. in t...