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1997
Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order,εdependent parabolic partial differential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the...

2014
Kouritzin, Michael, Ren, Y.X.
Let ℓ be Lebesgue measure and X=(Xt,t≥0;Pμ) be a supercritical, superstable process corresponding to the operator −(−Δ)α/2u+βu−ηu2 on Rd with constants β,η>0 and α∈(0,2]. Put View the MathML source, which for each smallθ is an a.s. convergent complexvalued martingale with limit View the MathML...

1997
Kouritzin, Michael, Dawson, Donald
A general Hilbertspacebased stochastic averaging theory is brought forth herein for arbitraryorder parabolic equations with (possibly long range dependent) random coefficients. We use regularity conditions onView the MathML sourcewhich are slightly stronger than those required to prove...

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...

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...

2008
Kouritzin, Michael, Newton, Fraser, Orsten, Sterling, Wilson, Daniel
Classification of data as true or fabricated has applications in fraud detection and verification of data samples. In this paper, we apply nonlinear filtering to a simplified frauddetection problem: classifying coin flip sequences as either real or faked. On the way, we propose a method for...

2004
McCrosky, Jesse, Kouritzin, Michael, Blount, Douglas
A hybrid weighted/interacting particle filter, the selectively resampling particle (SERP) filter, is used to detect and track an unknown number of independent targets on a onedimensional \"racetrack\" domain. The targets evolve in a nonlinear manner. The observations model a sensor positioned...

20131122
We address the missing analog of vague convergence in the weakconverge largedeviations analogy. Specifically, we introduce the weak Laplace principle and show it implies both the wellknown weak LDP and the Laplace principle lower bound. Both the weak LDP and weak Laplace principle hold in...

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...

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...