engleski

Statistical inference for reciprocal gamma diffusion process

We consider the problem of parameter estimation for an ergodic diffusion with reciprocal gamma invariant distribution. Spectral decomposition of the transition density of such a Markov process is presented in terms of a finite sum over the discrete spectrum and an integral over the essential spectrum of the negative infinitesimal generator of reciprocal gamma diffusion. Consistency and asymptotical normality of proposed estimators are presented. Based on the Stein equation for reciprocal gamma diffusion and Bessel polynomials, the hypothesis testing procedure is considered.

Asymptotic normality; Bessel polynomials; Consistency; Heavy-tailed distribution; Martingale estimation equation; Method of moments; Pearson equation; Reciprocal gamma distribution; Reciprocal gamma diffusion; Stationary distribution; Stein equation; Stochastic differential equation.

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