正倒向随机微分方程的参数估计

Parameter estimation on forward-backward stochastic differential equations

本文的研究目标是离散观测下正倒向随机微分方程中未知参数的估计及其性质.作为第一步,本文考虑一个线性模型.本文先导出两个状态过程的关系式,进而找到离散观测数据的似然函数.最后详细讨论最大似然估计量的相合性和渐近正态性.

This work aims at parameter estimation for discretely observed forward-backward stochastic differential equations.As the first step,we consider a linear model in this paper.The relationship between the forward and backward state processes is derived and hence the likelihood function with respect to discrete observations is determined.The consistency and asymptotic normality of the maximum likelihood estimator are discussed in details.