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Maximum likelihood estimator for hidden Markov models in continuous time
 Stat. Inference Stoch. Process
, 2009
"... Abstract. The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to I.Ibragimov and R.Khasminskii [14], consistency, asymptoti ..."
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Abstract. The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to I.Ibragimov and R.Khasminskii [14], consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity conditions on the chain. 1.
THE STABILITY OF CONDITIONAL MARKOV PROCESSES AND MARKOV CHAINS IN RANDOM ENVIRONMENTS By Ramon van Handel
, 801
"... We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this conditional signal is weakly ergodic when the signal is ergod ..."
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We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this conditional signal is weakly ergodic when the signal is ergodic and the observations are nondegenerate. This permits a delicate exchange of the intersection and supremum of σfields, which is key for the stability of the nonlinear filter and partially resolves a longstanding gap in the proof of a result of Kunita [J. Multivariate Anal. 1 (1971) 365–393]. A similar result is obtained also in the continuous time setting. The proofs are based on an ergodic theorem for Markov chains in random environments in a general state space. 1. Introduction. Consider
École doctorale nO432: SMI Sciences des Métiers de l’ingénieur
"... pour obtenir le grade de docteur délivré par l’École nationale supérieure des mines de Paris Spécialité « Mathématiques et Automatique » présentée et soutenue publiquement par Hadis AMINI le 27 septembre 2012 Stabilisation des systèmes quantiques à temps discrets et stabilité des filtres quantiques ..."
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pour obtenir le grade de docteur délivré par l’École nationale supérieure des mines de Paris Spécialité « Mathématiques et Automatique » présentée et soutenue publiquement par Hadis AMINI le 27 septembre 2012 Stabilisation des systèmes quantiques à temps discrets et stabilité des filtres quantiques à temps continus Directeur de thèse: Pierre ROUCHON Coencadrant de la thèse: Mazyar MIRRAHIMI
InformationDriven Pricing Kernel Models
, 2013
"... This thesis presents a range of related pricing kernel models that are driven by incomplete information about a series of future unknowns. These unknowns may, for instance, represent fundamental macroeconomic, political or social random variables that are revealed at future times. They may also repr ..."
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This thesis presents a range of related pricing kernel models that are driven by incomplete information about a series of future unknowns. These unknowns may, for instance, represent fundamental macroeconomic, political or social random variables that are revealed at future times. They may also represent latent or hidden factors that are revealed asymptotically. We adopt the informationbased approach of Brody, Hughston and Macrina (BHM) to model the information processes associated with the random variables. The market filtration is generated collectively by these information processes. By directly modelling the pricing kernel, we generate informationsensitive arbitragefree models for the term structure of interest rates, the excess rate of return required by investors, and security prices. The pricing kernel is modelled by a supermartingale to ensure that nominal interest rates remain nonnegative. To begin with, we primarily investigate finitetime pricing kernel models that are sensitive to Brownian bridge information. The BHM framework for the pricing of creditrisky instruments is extended