In this paper the authors give a definite meaning to any formal trigonometrical series and generalize it to an abstract Hilbert space. Then in the case L2(-∞,+∞) they discussed extensively the generalized expansion problem by Hermite functions, and applied to a non-strictly nonlinear hyperbolic system.
In this paper, based on random left truncated and right censored data the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function, which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.
JUMP DETECTION BY WAVELET IN NONLINEAR MODELS
Wavelets are applied to detection of the jump points of a regression function in nonlinear autoregressive model xt=T(xt-1)+εt. By checking the empirical wavelet coefficients of the data ,which have significantly large absolute values across fine scale levels, the number of the jump points and locations where the jumps occur are estimated. The jump heights are also estimated. All estimators are shown to be consistent.Wavelet method is also applied to the threshold AR(1) model(TAR(1)).The simple estimators of the thresholds are given,which are shown to be consistent.
This paper investigates the property of super-Brownian motion conditioned on non-extinction. The authors obtain a representation of Laplace functional for the weighted occupation time of this class of processes. By this, they get a result about the distribution of the support of it.
This paper studies the multi-dimensional Black-Scholes model of security val- uation. The extension of the Black-Scholes model implies the partial differential equation derived from an absence of arbitrage which the authors solve by using the Feynmen-Kac Formula. Then they compute its special example by solving the multi-variable partial differential equation.
An existence theorem is obtained for nonzero W1,2(RN) solutions of the following equations on RN −△u + b(x)u = f(x, u), x ∈ RN, where b is periodic for some variables and coercive for the others, f is superlinear.