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A law of the iterated logarithm for stochastic processes defined by differential equations with a small parameter
Download1994
Heunis, A.J., Kouritzin, Michael
Consider the following random ordinary differential equation: X˙ϵ(τ)=F(Xϵ(τ),τ/ϵ,ω)subject toXϵ(0)=x0, where {F(x,t,ω),t≥0} are stochastic processes indexed by x in Rd, and the dependence on x is sufficiently regular to ensure that the equation has a unique solution Xϵ(τ,ω) over the interval...
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1994
Heunis, A. J., Kouritzin, Michael
In this note we consider the almost sure convergence (as ϵ→0) of solution Xϵ(·), defined over the interval 0 ≤ τ ≤ 1, of the random ordinary differential equation View the MathML source Here {F(x, t, ω), t ≥ 0} is a strong mixing process for each x and (x, t) → F(x, t, ω) is subject to regularity...
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2003
Ballantyne, David, Wiersma, Jonathan, Kouritzin, Michael, Hailes, Jarett, Long, Hongwei
A hybrid weighted interacting particle filter, the selectively resampling particle filter (SERP), is used to detect and track multiple ships maneuvering in a region of water. The ship trajectories exhibit nonlinear dynamics and interact in a nonlinear manner such that the ships do not collide....
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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...
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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...
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2001
Ballantyne, David, Hoffman, John, Kouritzin, Michael
Particle-based 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 particle-based filtering techniques to real world problems....
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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...
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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...
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1997
Kouritzin, Michael, Dawson, Donald
A general Hilbert-space-based stochastic averaging theory is brought forth herein for arbitrary-order 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...
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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 one-dimensional \"racetrack\" domain. The targets evolve in a nonlinear manner. The observations model a sensor positioned...