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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...

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...

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...