# zbMATH — the first resource for mathematics

Large and moderate deviations in testing time inhomogeneous diffusions. (English) Zbl 1216.62131
Summary: This paper studies hypothesis testing in time inhomogeneous diffusion processes. With the help of large and moderate deviations for the log-likelihood ratio process, we give the negative regions and obtain the decay rates of the error probabilities. Moreover, we apply our results to hypothesis testing in the $$\alpha$$-Wiener bridge.

##### MSC:
 62M02 Markov processes: hypothesis testing 60F10 Large deviations 60J60 Diffusion processes
##### Keywords:
large deviations; log-likelihood ratio process
Full Text:
##### References:
 [1] Barczy, M.; Pap, G., Asymptotic behavior of maximum likelihood estimator for time inhomogeneous diffusion processes, Journal of statistical planning and inference, 140, 1576-1593, (2010), doi:10.1016/j.jspi.2009.12.016 · Zbl 1185.62147 [2] Barczy, M.; Pap, G., Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions, Journal of mathematical analysis and applications, 380, 405-424., (2011), arxiv:0810.2930v1 · Zbl 1215.60015 [3] Bishwal, J.P.N., Large deviations in testing fractional ornstein – uhlenbeck models, Statist. probab. lett., 78, 953-962, (2008) · Zbl 1144.62335 [4] Blahut, R.E., Hypothesis testing and information theory, IEEE trans. inform. theory, 20, 405-415, (1984) · Zbl 0305.62017 [5] Chiyonobu, T., Hypothesis testing for signal detection problem and large deviations, Nagoya math. J., 162, 187-203, (2003) · Zbl 0972.62064 [6] Dembo, A.; Zeitouni, D., Large deviations techniques and applications, (1998), Springer-Verlag · Zbl 0896.60013 [7] Florens-Landais, D.; Pham, H., Large deviations in estimate of an ornstein – uhlenbeck model, J. appl. probab., 36, 60-77, (1999) · Zbl 0978.62070 [8] Gepeev, P.V.; Küchler, U., On large deviations in testing ornstein – uhlenbeck-type models, Statist. inference stoch. process., 11, 143-155, (2008) · Zbl 1204.62144 [9] Jiang, H., Moderate deviations for parameter estimation in some time inhomogeneous diffusions, J. statist. plann. inference, 10, 3665-3674, (2009) · Zbl 1168.62374 [10] Kutoyants, Y.A., Statistical inference for ergodic diffusion process, (2003), Springer [11] Zhao, S.J.; Gao, F.Q., Large deviations in testing Jacobi model, Statist. probab. lett., 80, 34-41, (2010) · Zbl 1386.60103
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.