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2002
Kim, Surrey, Kouritzin, Michael, Ballantyne, David
Particlebased nonlinear filters have proven to be effective and versatile methods for computing approximations to difficult filtering problems. We introduce a novel hybrid particle method, thought to possess an excellent compromise between the unadaptive nature of the weighted particle methods...

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...

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...

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...

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...

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,...

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....

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...

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...