Quadratic Variation for a Class of $L \log^+ L$-Bounded Two-parameter Martingales

A value - distribution criterion for the class L log L and some related questions

Estimation of quadratic variation for two-parameter diffusions

Abstract In this paper we give a central limit theorem for the weighted quadratic variations process of a two-parameter Brownian motion. As an application, we show that the discretized quadratic variations [ns] i=1 [nt] j=1 |∆i,jY | of a twoparameter diffusion Y = (Y(s,t))(s,t)∈[0,1]2 observed on a regular grid Gn is an asymptotically normal estimator of the quadratic variation of Y as n goes t...

WEIGHTS AND L log L

Minimax Estimator of a Lower Bounded Parameter of a Discrete Distribution under a Squared Log Error Loss Function

The problem of estimating the parameter ?, when it is restricted to an interval of the form , in a class of discrete distributions, including Binomial Negative Binomial discrete Weibull and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of with respect to a two points boundary supported prior is minimax under squared log error loss function....

Quadratic Variation of Functionals of Two-Parameter Wiener Process

Let [W(s, t): (s, t) E R+7, R+2 = [0, co) x [0, co), be the standard twoparameter Wiener process defined on a complete probability space (Q, F, P), i.e., a Gaussian stochastic process with EW(s, t) = 0 and EW(s, t) W(s’, t’) = Min(s, s’) Min(t, t’). We shall also assume, as we may do without restricting the generality, that W(s, t; UJ) is sample path continuous, i.e., for each w, W(.; U) is a c...