Let (ξn)n≥1 be the polygonal partial sums processes built on the linear processes Xn = ∑ i≥0 ai( n−i), n ≥ 1, where ( i)i∈Z are i.i.d., centered random elements in some separable Hilbert space H and the ai’s are bounded linear operators H → H, with ∑i≥0‖ai‖ < ∞. We investigate functional central limit theorem for ξn in the Hölder spaces H o ρ(H) of functions x : [0, 1] → H such that ‖x(t+ h) − ...

Using elliptic and parabolic regularity results in $L^p$-spaces generalized Dirichlet form theory, we construct for every starting point weak solutions to SDEs $\mathbb{R}^d$ up their explosion times including the following conditions. For arbitrary but fixed $p>d$ diffusion coefficient $A=(a_{ij})_{1\le i,j\le d}$ is locally uniformly strictly with functions $a_{ij}\in H^{1,p}_{loc}(\mathbb{R}...

We propose a new subgradient-type method for minimizing extremely large-scale nonsmooth convex functions over “simple” domains. The characteristic features of the method are (a) the possibility to adjust the scheme to the geometry of the feasible set, thus allowing to get (nearly) dimension-independent (and nearly optimal in the large-scale case) rate-of-convergence results for minimization of ...

Let E be a real q-uniformly smooth Banach space with constant dq, q ≥ 2. Let T : E → E and G : E → E be a nonexpansive map and an η-strongly accretive map which is also κ-Lipschitzian, respectively. Let {λn} be a real sequence in 0, 1 that satisfies the following condition: C1: limλn 0 and ∑ λn ∞. For δ ∈ 0, qη/dqk 1/ q−1 and σ ∈ 0, 1 , define a sequence {xn} iteratively in E by x0 ∈ E, xn 1 Tn...

We consider initial value/boundary value problems for fractional diffusion-wave equation: ∂ α t u(x, t) = Lu(x, t), where 0 < α ≤ 2, where L is a symmetric uniformly elliptic operator with t-independent smooth coefficients. First we establish the unique existence of ths weak solutions and the asymptotic behaviour as the time t goes to ∞ and the proofs are based on the eigenfunction expansions. ...

and Applied Analysis 3 to a fixed point of the mapping T , which is also a solution of VI 1.5 defined on the set of fixed points of T . As direct consequences, we obtain the unique minimum-norm fixed point of T . Namely, we find the unique solution of the quadratic minimization problem: ‖x̃‖ min{‖x‖ : x ∈ Fix T }. 2. Preliminaries and Lemmas Throughout this paper, when {xn} is a sequence inH, xn...

1. GENERAL FORM OF FINITE VOLUME METHODS We consider vertex-centered finite volume methods for solving diffusion type elliptic equation (1) −∇ · (K∇u) = f in Ω, with suitable Dirichlet or Neumann boundary conditions. Here Ω ⊂ R is a polyhedral domain (d ≥ 2), the diffusion coefficient K(x) is a d× d symmetric matrix function that is uniformly positive definite on Ω with components in L∞(Ω), and...