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Studying the stability of partially observed Markov decision processes (POMDPs) with respect to perturbations in either transition or observation kernels is a significant problem. While asymptotic robustness/stability results as approximate…
In this paper, a backward map is introduced for the purposes of analysis of the nonlinear (stochastic) filter stability. The backward map is important because the filter-stability in the sense of $\chisq$-divergence follows from showing a…
Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the nonasymptotic,…
The problem of stability of the optimal filter is revisited. The optimal filter (or filtering process) is the conditional probability of the current state of some stochastic process (the signal process), given both present and past values…
This paper is concerned with the problem of nonlinear filter stability of ergodic Markov processes. The main contribution is the conditional Poincar\'e inequality (PI), which is shown to yield filter stability. The proof is based upon a…
Exponential stability of the nonlinear filtering equation is revisited, when the signal is a finite state Markov chain. An asymptotic upper bound for the filtering error due to incorrect initial condition is derived in the case of slowly…
The nonlinear filtering equation is said to be stable if it ``forgets'' the initial condition. It is known that the filter might be unstable even if the signal is an ergodic Markov chain. In general, the filtering stability requires…
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under…
This paper discusses particle filtering in general hidden Markov models (HMMs) and presents novel theoretical results on the long-term stability of bootstrap-type particle filters. More specifically, we establish that the asymptotic…
This paper is concerned with the problem of nonlinear (stochastic) filter stability of a hidden Markov model (HMM) with white noise observations. A contribution is the variance decay property which is used to conclude filter stability. For…
This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a…
In this review/tutorial article, we present recent progress on optimal control of partially observed Markov Decision Processes (POMDPs). We first present regularity and continuity conditions for POMDPs and their belief-MDP reductions, where…
Discrete time control systems whose dynamics and observations are described by stochastic equations are common in engineering, operations research, health care, and economics. For example, stochastic filtering problems are usually defined…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…
The exponential stability and the concentration properties of a class of extended Kalman-Bucy filters are analyzed. New estimation concentration inequalities around partially observed signals are derived in terms of the stability properties…
We establish conditions for an exponential rate of forgetting of the initial distribution of nonlinear filters in $V$-norm, path-wise along almost all observation sequences. In contrast to previous works, our results allow for unbounded…
We analyse the exponential stability properties of a class of measure-valued equations arising in nonlinear multi-target filtering problems. We also prove the uniform convergence properties w.r.t. the time parameter of a rather general…
A hidden Markov model is called observable if distinct initial laws give rise to distinct laws of the observation process. Observability implies stability of the nonlinear filter when the signal process is tight, but this need not be the…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…