Estimation of the characteristics of the jumps of a general Poisson-diffusion model

Rivista nelle classi B e B per il GEV Area 13 della VQR 2004-2010 ABSTRACT: We consider a filtered probability space with a standard Brownian motion W, a simple Poisson process N with constant intensity lambda > 0, and we consider the process Y such that Y_0 in R and dY_t=a_t dt + sigma_t dW_t + gamma_t dN_t; t>0; (1) where a, sigma are predictable bounded stochastic processes, and gamma is a predictable process which is bounded away from zero. A discrete record of n+1 observations {Y_0, Y_{t_1}, . . ., Y_{t_{n-1}}, Y_{t_n} } is available, with t_i=ih. Using such observations, we construct estimators of N_{t_i}, i=1, . . ., n, lambda and g_{tau_j}, where tau_j are the instants of jump within [0, nh]. They are consistent and asymptotically controlled when the number of observations increases and the step h tends to zero.