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Abstract: The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. [Copyright &y& Elsevier]

This paper deals with the management of multimode sensors such as multifunction radars. We consider the problems of multitarget radar scheduling formulated as multivariate partially observed Markov decision process (POMDPs). The aim is to compute the scheduling policy to determine which target to choose and how long to continue with this choice so as to minimize a cost function. We give sufficient conditions on the cost function, dynamics of the Markov chain target and observation probabilities so that the optimal scheduling policy has a threshold structure with respect to the multivariate TP2 ordering. This implies that the optimal parameterized policy can be estimated efficiently. We then present stochastic approximation algorithms for estimating the best multilinear threshold policy. [ABSTRACT FROM AUTHOR]

We consider the optimal sensor scheduling problem formulated as a partially observed Markov decision process (POMDP). Due to operational constraints, at each time instant, the scheduler can dynamically select one out of a finite number of sensors and record a noisy measurement of an underlying Markov chain. The aim is to compute the optimal measurement scheduling policy, so as to minimize a cost function comprising of estimation errors and measurement costs. The formulation results in a nonstandard POMDP that is nonlinear in the information state. We give sufficient conditions on the cost function, dynamics of the Markov chain and observation probabilities so that the optimal scheduling policy has a threshold structure with respect to a monotone likelihood ratio (MLR) ordering. As a result, the computational complexity of implementing the optimal scheduling policy is inexpensive. We then present stochastic approximation algorithms for estimating the best linear MLR order threshold policy. [ABSTRACT FROM AUTHOR]

This paper extends some adaptive schemes that have been developed for the Random Walk Metropolis algorithm to more general versions of the Metropolis-Hastings (MH) algorithm, particularly to the Metropolis Adjusted Langevin algorithm of Roberts and Tweedie (). Our simulations show that the adaptation drastically improves the performance of such MH algorithms. We study the convergence of the algorithm. Our proves are based on a new approach to the analysis of stochastic approximation algorithms based on mixingales theory. [ABSTRACT FROM AUTHOR]