The difference equations ξk = af(ξk−1) + εk, where (εk) is a square integrable difference martingale, and the differential equation dξ = −af(ξ)dt + dη, where η is a square integrable martingale, are considered. A family of estimators depending, besides the sample size n (or the observation period, if time is continuous) on some random Lipschitz functions is constructed. Asymptotic optimality of...

This paper is a continuation of [HT]. Let L be an imaginary CM field and let Π be a regular algebraic (i.e., Π∞ has the same infinitesimal character as an algebraic representation of the restriction of scalars from L to Q of GLn) cuspidal automorphic representation of GLn(AL) which is conjugate self-dual (Π ◦ c ∼= Π∨) and square integrable at some finite place. In [HT] it is explained how to at...

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...

In this paper we establish the existence of a square integrable occupation density for two classes of stochastic processes. First we consider a Gaussian process with an absolutely continuous random drift, and secondly we handle the case of a (Skorohod) integral with respect to the fractional Brownian motion with Hurst parameter H > 1 2 . The proof of these results uses a general criterion for t...

A prototype of the above situation is when H is L2( — °°, °° î N), i.e., the space of square integrable functions on the whole real axis whose values lie in some accessory Hubert space Nt U(t) is translation by t, and D+ is L%(0f oo ; N). THEOREM l. If D+ is outgoing for the group U(t), then H can be represented isometrically as L%(-~ oo, oo ; N) so that U(t) is translation and D+ is the space ...

Continuous wavelet transforms arising from the quasiregular representation of a semidirect product group G = R ⋊ H have been studied by various authors. Recently the attention has shifted from the irreducible case to include more general dilation groups H , for instance cyclic (more generally: discrete) or one-parameter groups. These groups do not give rise to irreducible square-integrable repr...

We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are based on a notion of pathwise functional derivative and yield a consistent estimator for the integrand in the martingale representation formula for any square-integrable functional of the solution of an SDE with path-dependent coeff...