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2008
In this paper, we give a direct derivation of the Duncan–Mortensen–Zakai filtering equation, without assuming right continuity of the signal, nor its filtration, and without the usual finite energy condition. As a consequence, the Fujisaki–Kallianpur–Kunita equation is also derived. Our results...

2011
Newton, Fraser, Kouritzin, Michael
A CAPTCHA is an automatically generated test designed to distinguish between humans and computer programs; specifically, they are designed to be easy for humans but difficult for computer programs to pass in order to prevent the abuse of resources by automated bots. They are commonly seen...

2013
Kouritzin, Michael, Wu, B., Newton, F.
Herein, we propose generating CAPTCHAs through random field simulation and give a novel, effective and efficient algorithm to do so. Indeed, we demonstrate that sufficient information about word tests for easy human recognition is contained in the site marginal probabilities and the...

2005
Kouritzin, Michael, Kim, H., Hu, Y., Ballantyne, D.
This paper addresses the problem of detecting and tracking an unknown number of submarines in a body of water using a known number of moving sonobuoys. Indeed, we suppose there are N submarines collectively maneuvering as a weakly interacting stochastic dynamical system, where N is a random...

20130910
The equivalences to and the connections between the modulusofcontinuity condition, compact containment and tightness on DE[a, b] with a < b are studied. The results within are tools for establishing tightness for probability measures on DE[a, b] that generalize and simplify prevailing results...

2001
Chan, Hubert, Kouritzin, Michael
Filtering is a method of estimating the conditional probability distribution of a signal based upon a noisy, partial, corrupted sequence of observations of the signal. Particle filters are a method of filtering in which the conditional distribution of the signal state is approximated by the...

2001
Ballantyne, David, Hoffman, John, Kouritzin, Michael
Particlebased nonlinear filters provide a mathematically optimal (in the limit) and sound method for solving a number of difficult filtering problems. However, there are a number of practical difficulties that can occur when applying particlebased filtering techniques to real world problems....

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...