In many applications (engineering, management, economy) one is led to control problems for stochastic systems : more precisely the state of the system is assumed to be described by the solution of stochastic differential equations and the control enters the coefficients of the equation. Using the dynamic programming principle E. Bellman [6] explained why, at least heuristically, the optimal cos...

A class of interacting superprocesses arising from branching particle systems with continuous spatial motions, called superprocesses with dependent spatial motion (SDSMs), has been introduced and studied in Wang [26] and Dawson et al. [8]. In this paper, we extend the model to allow discontinuous spatial motions. Under Lipschitz condition for coefficients, we show that under a proper rescaling,...

The purpose of this article is to giye an overview of some recent developments in optimal stochastic control theory. The field has expanded a great deal during the last 20 years. It is not possible in this overview to go deeply into any topic, and a number of interesting topics have been omitted entirely. The list of references includes several books, conference proceedings and survey articles....

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...

A class of quasilinear stochastic partial differential equations (SPDEs), driven by spatially correlated Brownian noise, is shown to become macroscopic (i.e., deterministic), as the length of the correlations tends to 0. The limit is the solution of a quasilinear partial differential equation. The quasilinear SPDEs are obtained as a continuum limit from the empirical distribution of a large num...

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 ...

This paper illustrates the main results of a spatio-temporal interpolation process PM10 concentrations at daily resolution using set 410 monitoring sites, distributed throughout Italian territory, for year 2015. The is based on Bayesian hierarchical model where spatial-component represented through Stochastic Partial Differential Equation (SPDE) approach with lag-1 temporal autoregressive compo...

We prove a Kramers-type law for metastable transition times for a class of onedimensional parabolic stochastic partial differential equations (SPDEs) with bistable potential. The expected transition time between local minima of the potential energy depends exponentially on the energy barrier to overcome, with an explicit prefactor related to functional determinants. Our results cover situations...

Using Wiener chaos expansion (WCE), we develop numerical algorithms for solving second-order linear parabolic stochastic partial differential equations (SPDEs). We propose a deterministic WCE-based algorithm for computing moments of the SPDE solutions without any use of the Monte Carlo technique. We also compare the proposed deterministic algorithm with two other numerical methods based on the ...