On mean discounted numbers of passage times in small balls of Ito processes observed at discrete times

Keywords: diffusion coefficient estimation, observation at stopping times, consistent se- quence of estimators, local asymptotic mixed normality, asymptotic variance, optimal

Keywords: Gaussian processes and local times, stochastic analysis & White noise theory, Wick-Itô integrals, Tanaka formulas, fractional and multifractional Brownian motions..

In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes.. The proof is based on

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Under the assumption that neither the time gaps nor their distribution are known, we provide an estimation method which applies when some transi- tions in the initial Markov chain X

Let h > 0.. Our second result concerns expectations of the number of times that an Itô process, observed at discrete times between 0 and a finite horizon T, visits

Red crosses: simulations; blue dashed line: large volume approximation (21). The domain is a cube of side 41, the target being in the middle of it. All the simulation points