论文标题
在部分观察到的跳跃扩散I.滤波方程
On partially observed jump diffusions I. The filtering equations
论文作者
论文摘要
本文是有关过滤的一系列论文的第一部分，以部分观察到的跳跃扩散，以满足Wiener过程和泊松Martingale测量驱动的随机微分方程。方程的系数仅满足适当的生长条件。鉴于有条件分布的时间演变的滤波过程过滤理论的一些结果扩展到跳跃扩散和方程，并在$ t $的情况下$ t $ ty $ t $ the $ t $ t $呈现了未观察到的未观察到的条件分布。
This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the equation only satisfy appropriate growth conditions. Some results in filtering theory of diffusion processes are extended to jump diffusions and equations for the time evolution of the conditional distribution and the unnormalised conditional distribution of the unobserved process at time $t$, given the observations until $t$, are presented.
