This paper develops the Bayesian model selection based on Bayes factor for a rich class of partially-observed micro-movement models of asset price. We focus on one recursive algorithm to calculateâ€¦ (More)

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 wordâ€¦ (More)

A general Hilbert-space-based stochastic averaging theory is brought forth in this note for arbitrary-order parabolic equations with (possibly long range dependent) random coe cients. We start withâ€¦ (More)

Many ltering applications are characterized by continuous state dynamics Xt = R t 0 m(Xs)ds + Wt + , discrete observations Yk = Ytk , and observation noise that is non-additive or non-Gaussian. Inâ€¦ (More)

Many stochastic approximation procedures result in a stochastic algorithm of the form 1 hk+l = h k + (bk A k h k ) , k for all IC = 1 , 2 , 3 . . . . . Here, { b k , IC = 1,2 ,3 , . . .} is aâ€¦ (More)

The paper studies the filtering problem for a non-classical framework: we assume that the observation equation is driven by a signal dependent noise. We show that the support of the conditionalâ€¦ (More)

Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order, "-dependent parabolic partial di erential equations is developed. Indeed, by directly developingâ€¦ (More)

Herein, we generalize and extend some standard results on the separation and convergence of probability measures. We use homeomorphism-based methods and work on incomplete metric spaces, Skorokhodâ€¦ (More)

Let ` be Lebesgue measure and X = (Xt, t â‰¥ 0;PÎ¼) be a supercritical, super-stable process corresponding to the operator âˆ’ (âˆ’âˆ†) u+Î²uâˆ’Î·u2 on IR with constants Î², Î· > 0 and Î± âˆˆ (0, 2]. Put Å´t(Î¸) = e(|Î¸|â€¦ (More)

Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that t â†’ Xt is a Markov process and we wish toâ€¦ (More)