# Search

• ### Convergence of Markov chain approximations to stochastic reaction diffusion equations.

2002

In the context of simulating the transport of a chemical or bacterial contaminant through a moving sheet of water, we extend a well-established method of approximating reaction-diffusion equations with Markov chains by allowing convection, certain Poisson measure driving sources and a larger...

2014

• ### Markov chain approximations to filtering equations for reflecting diffusion processes.

2004

Herein, we consider direct Markov chain approximations to the Duncan–Mortensen–Zakai equations for nonlinear filtering problems on regular, bounded domains. For clarity of presentation, we restrict our attention to reflecting diffusion signals with symmetrizable generators. Our Markov chains are...

• ### Strong approximation for cross-covariances of linear variables with long-range dependence.

1995

Suppose {εk, −∞ < k < ∞} is an independent, not necessarily identically distributed sequence of random variables, and {cj}∞j=0, {dj}∞j=0 are sequences of real numbers such that Σjc2j < ∞, Σjd2j < ∞. Then, under appropriate moment conditions on {εk, −∞ < k < ∞}, View the MathML source, View the...

• ### Rates for branching particle approximations of continuous discrete filters.

2005

Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that t→Xt is a Markov process and we wish to calculate the measure-valued process t→μt(⋅)≐P{Xt∈⋅|σ{Ytk, tk≤t}}, where tk=kɛ and Ytk is a distorted,...

2015-09-21

2014

• ### The Irreducible Characters of 2 x 2 Unitary Matrix Groups Over Finite Fields

2014-08-28

In this work we will construct the table of irreducible characters for the group of unitary 2 x 2 matrices over a finite field. The table and the methods for its construction will show interesting connections to the table and methods of construction of the table of irreducible characters for the...

• ### A graph theoretic approach to simulation and classification

2014

A new class of discrete random fields designed for quick simulation and covariance inference under inhomogenous conditions is introduced and studied. Simulation of these correlated fields can be done in a single pass instead of relying on multi-pass convergent methods like the Gibbs Sampler or...

• ### Rates of convergence in a central limit theorem for stochastic processes defined by differential equations with a small parameter

1992

Let μ be a positive finite Borel measure on the real line R. For t ≥ 0 let et · E1 and E2 denote, respectively, the linear spans in L2(R, μ) of {eisx, s > t} and {eisx, s < 0}. Let θ: R → C such that ∥θ∥ = 1, denote by αt(θ, μ) the angle between θ · et · E1 and E2. The problems considered here...

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