In this paper we study the connection between matrix measures and random walks with a block tridiagonal transition matrix. We derive sufficient conditions such that the blocks of the n-step block tridiagonal transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued spectral measure. Several stochastic properties of the processes are characterized by m...

We introduce a technique called "precomputation of integrals" that makes it possible to compute conditional expectations in dynamic stochastic models in the initial stage of the solution procedure. This technique can be applied to any set of equations that contains conditional expectations, in particular, to the Bellman and Euler equations. After the integrals are precomputed, we can solve stoc...

We study Monte Carlo approximations to high dimensional parameter dependent integrals. We survey the multilevel variance reduction technique introduced by the author in [4] and present extensions and new developments of it. The tools needed for the convergence analysis of vector-valued Monte Carlo methods are discussed, as well. Applications to stochastic solution of integral equations are give...

In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales defined on locally convex space $\Phi$. Our construction the integral is based tensor products topological vector spaces and property good integrators real-valued semimartingales. This further developed in case where $\Phi$ complete, barrelled, nuclear space, obtain complete descript...

We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of π or log(2). In order to perform these simplifications, we view the series as specializations of generating series. For these generating series, we derive integral representations in terms of root-valued iterated integrals. Using substitutions, we express the inter...

In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

We investigate the asymptotic behavior of a stochastic version of the forward-backward splitting algorithm for finding a zero of the sum of a maximally monotone set-valued operator and a cocoercive operator in Hilbert spaces. Our general setting features stochastic approximations of the cocoercive operator and stochastic perturbations in the evaluation of the resolvents of the set-valued operat...

Aim of this paper is to study the parabolic Volterra equation u(t) + (b ∗Au)(t) = (QB)(t), t ≥ 0, on a separable Hilbert space. Throughout this work the operator −A is assumed to be a differential operator like the Laplacian, the elasticity operator, or the Stokes operator. The random disturbance Q1/2BH is modeled to be a system independent vector valued fractional Brownian motion with Hurst pa...