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国家教育部博士点基金(20060254006)

作品数:2 被引量:5H指数:1
相关作者:王金德陈萍更多>>
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Wavelet estimation of the diffusion coefficient in time dependent diffusion models被引量:4
2007年
The estimation problem for diffusion coefficients in diffusion processes has been studied in many papers,where the diffusion coefficient function is assumed to be a 1-dimensional bounded Lipschitzian function of the state or the time only.There is no previous work for the nonparametric estimation of time-dependent diffusion models where the diffusion coefficient depends on both the state and the time.This paper introduces and studies a wavelet estimation of the time-dependent diffusion coefficient under a more general assumption that the diffusion coefficient is a linear growth Lipschitz function.Using the properties of martingale,we translate the problems in diffusion into the nonparametric regression setting and give the Lr convergence rate.A strong consistency of the estimate is established.With this result one can estimate the time-dependent diffusion coefficient using the same structure of the wavelet estimators under any equivalent probability measure.For example,in finance,the wavelet estimator is strongly consistent under the market probability measure as well as the risk neutral probability measure.
Ping CHEN~(1,2+) Jin-de WANG~1 1 Department of Mathematics,Nanjing University,Nanjing 210093,China
关键词:WAVELETTIME-DEPENDENTCOEFFICIENTCONDITIONSTRONGCONSISTENCY
时变扩散模型中扩散系数的小波估计被引量:1
2007年
本文构造了一种时变扩散系数的小波估计.与文献中一维扩散系数的非参数估计问题相比,放宽了对扩散系数的限制,假定扩散系数为满足线性增长条件的Lipschitz函数.利用鞅的性质,将扩散方程中的估计问题转化为非参数回归模型,并给出了估计量的L^r收敛速度.在此基础上证明了估计量的强相合性.利用强相合性,可以在任何概率测度下用统一方法构造的小波估计量来估计时变扩散系数.
陈萍王金德
关键词:小波估计线性增长条件强收敛
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