论文标题
在部分观察到的跳跃扩散III中。过滤密度的规律性
On partially observed jump diffusions III. Regularity of the filtering density
论文作者
论文摘要
与Wiener流程和Poisson Martingale测量的驱动，与部分观察到的跳跃扩散模型$（z_t）_ {t \ in [0，t]} =（x_t，y_t）_ {t \ in [0，y_t）_ {t \ in [0，t]} =（x_t，y_t）_ {t \ in [0，t]} =（x_t，y_t）_ {t \ in [0，t]} =（t \ in [0，t]} $相关的过滤方程。 Building on results from two preceding articles on the filtering equations, the regularity of the conditional density of the signal $X_t$, given observations $(Y_s)_{s\in [0,t]}$, is investigated, when the conditional density of $X_0$ given $Y_0$ exists and belongs to a Sobolev space, and the coefficients satisfy appropriate smoothness and growth conditions.
The filtering equations associated to a partially observed jump diffusion model $(Z_t)_{t\in [0,T]}=(X_t,Y_t)_{t\in [0,T]}$, driven by Wiener processes and Poisson martingale measures are considered. Building on results from two preceding articles on the filtering equations, the regularity of the conditional density of the signal $X_t$, given observations $(Y_s)_{s\in [0,t]}$, is investigated, when the conditional density of $X_0$ given $Y_0$ exists and belongs to a Sobolev space, and the coefficients satisfy appropriate smoothness and growth conditions.
