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August 2020 On classical and Bayesian asymptotics in state space stochastic differential equations
Trisha Maitra, Sourabh Bhattacharya
Braz. J. Probab. Stat. 34(3): 629-657 (August 2020). DOI: 10.1214/19-BJPS439


In this article, we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our asymptotic theory to random effects models based on systems of state space SDEs, covering both independent and identical and independent but non-identical collections of state space SDEs. We also address asymptotic inference in the case of multidimensional linear random effects, and in situations where the data are available in discretized forms. It is important to note that asymptotic inference, either in the classical or in the Bayesian paradigm, has not been hitherto investigated in state space SDEs.


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Trisha Maitra. Sourabh Bhattacharya. "On classical and Bayesian asymptotics in state space stochastic differential equations." Braz. J. Probab. Stat. 34 (3) 629 - 657, August 2020.


Received: 1 December 2017; Accepted: 1 March 2019; Published: August 2020
First available in Project Euclid: 20 July 2020

zbMATH: 07232916
MathSciNet: MR4124544
Digital Object Identifier: 10.1214/19-BJPS439

Keywords: asymptotic normality , Kullback–Leibler divergence , posterior consistency , random effects , state space stochastic differential equations , Stochastic stability

Rights: Copyright © 2020 Brazilian Statistical Association


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Vol.34 • No. 3 • August 2020
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