Journal ArticleDOI
Statistical Estimation of Switching Systems under Transient Conditions and Applications in Reliability Models
Vladimir V. Anisimov,G. Guleryuz +1 more
TLDR
In this paper, a new approach is proposed to problems of asymptotic parameter estimation in stochastic switching systems, which allows one to investigate the properties of estimates of parameters constructed from observed trajectories.Abstract:
A new approach is proposed to problems of asymptotic parameter estimation in stochastic switching systems. In this approach, results on the asymptotic behavior of solutions of stochastic equations and theorems of the type of averaging are used for switching processes. This approach allows one to investigate asymptotic properties of estimates of parameters constructed from observed trajectories for a numerous class of stochastic systems with regular behaviors of trajectories under stationary and transient conditions.read more
Citations
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Dissertation
Parameter estimation in switching stochastic models
TL;DR: Gürler et al. as mentioned in this paper proposed an approach to statistical parameter estimation when an estimator is constructed by the trajectory observations of a stochastic system and apply the approach to reliability models.
References
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Book
Statistical estimation : asymptotic theory
TL;DR: In this article, the authors consider the problem of asymptotically optimal estimators and compare different estimators in terms of the mean square deviation from the parameter or perhaps in some other way.
Journal ArticleDOI
Martingale estimation functions for discretely observed diffusion processes
Bo Martin Bibby,Michael Sørensen +1 more
TL;DR: In this paper, the authors consider three different martingale estimating functions based on discrete-time observations of a diffusion process and show that all three estimators result in consistent and asymptotically normally distributed estimators when the underlying diffusion is ergodic.
Journal ArticleDOI
Switching processes: Averaging principle, diffusion approximation and applications
TL;DR: In this paper, a special class of processes with discrete interference of chance-switching processes (SP) is introduced, and limit theorems for these processes in the case of fast switching (averaging principle and diffusion approximation) are proved for the models with simple and semi-Markov switchings.