## Moderate deviations for squared radial Ornstein-Uhlenbeck process.(English)Zbl 1163.62309

Summary: We study moderate deviations for maximum likelihood estimators of parameters in generalized squared radial Ornstein-Uhlenbeck processes. Moderate deviation principles for the two parameters are established.

### MSC:

 62F12 Asymptotic properties of parametric estimators 62M05 Markov processes: estimation; hidden Markov models 60F10 Large deviations 62N05 Reliability and life testing
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### References:

 [1] Bercu, B.; Rouault, A., Sharp large deviations for the ornstein – uhlenbeck, Theory probab. appl., 46, 1-19, (2002) · Zbl 1101.60320 [2] Dembo, A.; Zeitouni, D., Large deviations techniques and applications, (1998), Springer-Verlag · Zbl 0896.60013 [3] Florens-Landais, D.; Pham, H., Large deviations in estimate of an ornstein – uhlenbeck model, J. appl. probab., 36, 60-77, (1999) · Zbl 0978.62070 [4] Overbeck, L., Estimation for continuous branching processes, Scand. J. statist., 25, 111-126, (1998) · Zbl 0905.62083 [5] Pitman, J.; Yor, M., A decomposition of Bessel bridges, Z. wahrscheinlichkeitstheor. verwandte geb., 59, 425-457, (1982) · Zbl 0484.60062 [6] Revuz, D.; Yor, M., Continuous martingales and Brownian motion, (1999), Springer · Zbl 0917.60006 [7] Watson, G.N., A treatise on the theory of Bessel function, (1995), Cambridge University Press · Zbl 0849.33001 [8] Yor, M., () [9] Zani, M., Large deviations for squared radial ornstein – uhlenbeck processes, Stochastic process. appl., 102, 25-42, (2002) · Zbl 1075.62535 [10] Zani, M., 2000. Grandes déviations pour des fonctionnelles issues de la statistique des processus. Thèse, Orsay
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