Research Publications (Mathematical and Statistical Sciences)
Items in this Collection
 31Kouritzin, Michael
 4Ballantyne, David
 4Kim, Surrey
 4Newton, Fraser
 3Kouritzin, Michael A.
 3Long, H.
 38Mathematical and Statistical Sciences, Department of
 38Mathematical and Statistical Sciences, Department of/Research Publications (Mathematical and Statistical Sciences)
 1Music, Department of
 1Music, Department of/Journal Articles (Music)
 1Campus SaintJean
 1Campus SaintJean/Research Publications (Campus SaintJean)

20190504
We identify seventone (heptatonic) scales as a sequence of minor and major thirds, where we use a zero to indicate a minor third and a one for a major third. Each proper seventone scale is then represented by a {0,1}sequence of length seven. On these {0,1}sequences we define group operations...

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...

2014
Wu, B., Newton, F., Kouritzin, Michael A.
A new class of discrete random fields designed for quick simulation and covariance inference under inhomogenous conditions is introduced and studied. Simulation of these correlated fields can be done in a single pass instead of relying on multipass convergent methods like the Gibbs Sampler or...

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....

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...

2000
Ballantyne, David, Chan, Hubert, Kouritzin, Michael
Particle approximations are used to track a maneuvering signal given only a noisy, corrupted sequence of observations, as are encountered in target tracking and surveillance. The signal exhibits nonlinearities that preclude the optimal use of a Kalman filter. It obeys a stochastic differential...

2004
Zhao, Xingqiu, Long, Hongwei, McCrosky, Jesse, Kim, Surrey, Kouritzin, Michael
In this paper, we discuss multitarget tracking for a submarine model based on incomplete observations. The submarine model is a weakly interacting stochastic dynamic system with several submarines in the underlying region. Observations are obtained at discrete times from a number of sonobuoys...

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...

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...

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...