论文标题
在部分观察到的跳跃扩散II。过滤密度
On partially observed jump diffusions II. The filtering density
论文作者
论文摘要
部分观察到的跳跃扩散$ z =（x_t，y_t）_ {t \ in [0，t]} $由Wiener过程驱动的随机微分方程给出，当方程式满足适当的Lipschitz和生长条件时，请考虑由Wiener过程和Poisson Martingale措施。在一般条件下，证明未观察到的$ x_t $的条件密度给定观测值$（y_s）_ {s \ in [0，t]} $存在，并且如果有$ x_0 $的条件密度为$ y_0 $，并且属于$ y_0 $，则属于$ l_p $。
A partially observed jump diffusion $Z=(X_t,Y_t)_{t\in[0,T]}$ given by a stochastic differential equation driven by Wiener processes and Poisson martingale measures is considered when the coefficients of the equation satisfy appropriate Lipschitz and growth conditions. Under general conditions it is shown that the conditional density of the unobserved component $X_t$ given the observations $(Y_s)_{s\in[0,T]}$ exists and belongs to $L_p$ if the conditional density of $X_0$ given $Y_0$ exists and belongs to $L_p$.
