BFS 2002

Poster Presentation

Estimation of the characteristics of jump of a general poisson-diffusion model

Cecilia Mancini

On a filtered probability space where W and N are respectively a standard Brownian motion and a simple Poisson process with constant intensity $\lambda >0$ we consider the process $Y$ such that $Y_0\in \R$ and \beqlab{modello} dY_t=a_tdt+\sigma_tdW_t+ \gamma_{t}dN_t,\; t\leq T,\eeq where $a$, $\sigma$ are predictable bounded stochastic processes, and $\gamma$ is a predictable process which keeps away from zero. A discrete record of $n+1$ observations $\{Y_{0}, Y_{h},...,Y_{(n-1)h},Y_{nh}\}$ is available, with $nh=T$. Using such observations we construct estimators of $N_{t_i}(\omega), i=1,..., n$, $\lambda$ and $\gamma_{\tau_j}(\omega)$, where $\tau_j$ are the instants of jump within $[0,T].$ They are consistent and asymptotically controlled when the number of observations increases and contemporaneously the step $h$ between them tends to zero.