Parallel SAS processes, multiple threads within a single SAS process, parallel SAS servers, distributed computing, grid computing, cluster computing – how might all of these choices affect the way that you develop your client/server SAS applications? This paper will address some of these areas and what you should understand when you develop or run client/server SAS applications in these environ...

In this paper, we first study the existence-uniqueness and large deviation estimate of solutions for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then, we apply them to a large class of semilinear stochastic partial differential equations (SPDE) driven by Brownian motions as well as by fractional Brownian motions, and obtain the existence of unique max...

In this paper we study the solvability of backward doubly stochastic differential equations (BDSDEs for short) with polynomial growth coefficients and their connections with SPDEs. The corresponding SPDE is in a very general form, which may depend on the derivative of the solution. We use Wiener-Sobolev compactness arguments to derive a strongly convergent subsequence of approximating SPDEs. Fo...

Stochastic partial differential equations (SPDE) on graphs were recently introduced by Cerrai and Freidlin (Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 865–899). This class of stochastic in infinite dimensions provides a minimal framework for the study effective dynamics much more complex systems. However, how they emerge from microscopic individual-based models is still poorly understood...

We deal with the Sobolev space theory for stochastic partial differential equation (SPDE) driven by Wiener processes $$\begin{aligned} \partial _{t}^{\alpha }u=\left( \phi (\varDelta ) u +f(u) \right) + _t^\beta \sum _{k=1}^\infty \int _0^t g^k(u)\,dw_s^k, \quad t>0, \,x\in {\mathbb {R}}^d \end{aligned}$$ as well SPDE space-time white noise ^{\alpha }_{t}u=\phi )u f(u) ^{\beta -1}_{t}h(u) {\dot...

Perturbations to Markov chains and Markov processes are considered. The unperturbed problem is assumed to be geometrically er-godic in the sense usually established through use of Foster-Lyapunov drift conditions. The perturbations are assumed to be uniform, in a weak sense, on bounded time intervals. The long-time behaviour of the perturbed chain is studied. Applications are given to numerical...

In this paper we study well-posedness of a second order SPDE with multiplicative noise on the torus T = [0, 2π]. The equation is considered in L((0, T )×Ω;L(T)) for p, q ∈ (1,∞). It is well-known that if the noise is of gradient type, one needs a stochastic parabolicity condition on the coefficients for well-posedness with p = q = 2. In this paper we investigate whether the well-posedness depen...

In this paper we rigorously derive stochastic amplitude equations for a rather general class of SPDEs with quadratic nonlinearities forced by small additive noise. Near a change of stability we use the natural separation of time-scales to show that the solution of the original SPDE is approximated by the solution of an amplitude equation, which describes the evolution of dominant modes. Our res...

In this paper we shall discuss an extension to Gaussian process (GP) regression models, where the measurements are modeled as linear functionals of the underlying GP and the estimation objective is a general linear operator of the process. We shall show how this framework can be used for modeling physical processes involved in measurement of the GP and for encoding physical prior information in...

The aim of this paper is to extend the usual framework of SPDE with monotone coefficients to include a large class of cases with merely locally monotone coefficients. This new framework is conceptually not more involved than the classical one, but includes many more fundamental examples not included previously. Thus our main result can be applied to various types of SPDEs such as stochastic rea...