Search
Skip to Search Results
2002
In the context of simulating the transport of a chemical or bacterial contaminant through a moving sheet of water, we extend a wellestablished method of approximating reactiondiffusion equations with Markov chains by allowing convection, certain Poisson measure driving sources and a larger...

2004
Kouritzin, Michael, Long, H., Sun, W.
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...

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...

2005
Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuousdiscrete filtering problems. Suppose that t→Xt is a Markov process and we wish to calculate the measurevalued process t→μt(⋅)≐P{Xt∈⋅σ{Ytk, tk≤t}}, where tk=kɛ and Ytk is a distorted,...

Rates of convergence in a central limit theorem for stochastic processes defined by differential equations with a small parameter
Download1992
Kouritzin, Michael, Heunis, A.J.
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...

20140605
The classical particle filter, introduced in 1993, approximates the normalized filter directly. It has two defiencies, over resampling and the inability to distinguish models, the former of which was overcome but the later is fundamental. Conversely, the weighted particle filter, motivated by the...

2002
Kouritzin, Michael, Bauer, Will, Kim, Surrey
Predicting the future state of a random dynamic signal based on corrupted, distorted, and partial observations is vital for proper realtime control of a system that includes time delay. Motivated by problems from Acoustic Positioning Research Inc., we consider the continual automated...