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The stability of a model of the dynamics of a class of split-gate radar range trackers is considered, under both deterministic and stochastic target models. The emphasis is on stability as a means toward studying the dynamics of the tracker in the presence of both an actual target and a decoy target. The model employed reflects Automatic Gain Control action for noise attenuation as well as nonlinear...
This work is concerned with asymptotic properties of singularly perturbed Markov chains in discrete time with finite state spaces. We study asymptotic expansions of the probability distribution vectors and derive a mean square estimate on a sequence of occupation measures. Assuming that the state space of the underlying Markov chain can be decomposed into several groups of recurrent states and a group...
This paper reports a tight bound on the data capacity a feedback channel must provide in order to stabilize a right half-plane pole of a linear, time-invariant control system. The proof is constructive, and involves considering a general class of quantized control realizations of classical feedback designs. Even for the coarsest quantizations—with two-element control input sets, which we refer to...
Let O be an open bounded smooth domain of ℝn, and let Γ = αO be its boundary. We denote by n the normal vector at the boundary Γ, oriented towards the outside of O. Let us consider the canonical process $$\begin{gathered} \Omega = C^0 ([0,\infty );\bar O), \hfill \\ y(t,w) \equiv w(t), if w \in \Omega , \hfill \\ \mathfrak{F}^t = \sigma (y(s),0 \leqslant s \leqslant t). \hfill...
We consider a Black-Scholes market in which the underlying economy, as modelled by the parameters and volatility of the processes, switches between a finite number of states. The switching is modelled by a hidden Markov chain. European options are priced and a Black-Scholes equation obtained.
Under some reasonable conditions imposed on the moving average part C(z)wk of the multi-dimensional system A(z)yk = C(z)wk it is shown that for stability of A(z), which means that all zeros of det A(z) are outside the closed unit disk, the necessary and sufficient condition is the stability of the system in the mean square sense, by which it is meant that the long...
The aim of this contribution is to describe main features in the development of system identification, in the sense of modelling from time series data. Given the restrictions in space, such an effort is necessarely fragmentary. Clearly, subjective judgements cannot be avoided. System identification has been developed in a number of different scientific communities, the most important of which are...
Max-plus stochastic processes are counterparts of Markov diffusion processes governed by Ito sense stochastic differential equations. In this framework, expectations are linear operations with respect to max-plus arithmetic. Max-plus stochastic control problems are considered, in which a minimizing control enters the state dynamics and running cost. The minimum max-plus expected cost is equal to the...
An extension of the classical Merton model with consumption is considered when the diffusion coefficient of the asset prices depends on some economic factor. The objective is to maximize total expected discounted HARA utility of consumption. Optimal controls are provided as well as a characterization of the value function in terms of the associated Hamilton-Jacobi-Bellman equation.
The time-varying dynamics and non-stationarity of epileptic seizures makes their detection difficult. Osorio et. al. in ([1]) proposed an adaptable seizure detection algorithm (‘SDA’), however, that has had great success. In this presentation, we begin with an overview of the original detection algorithm’s architecture, describing its degrees of freedom that provide flexibility and outline a procedure...
We consider simultaneous perturbation stochastic approximation (SPSA) methods applied to noise-free problems in optimization and adaptive control. More generally, we consider discrete-time fixed gain stochastic approximation processes that are defined in terms of a random field that is identically zero at some point θ*. The boundedness of the estimator process is enforced by a resetting mechanism...
This paper examines the Shannon capacity of the single-user, multiple-input, multiple-output (MIMO) Poisson channel with peak and average transmit power constraints. The MIMO Poisson channel is a good model for the physical layer of a multi-aperture optical communication system that operates in the shot-noise-limited regime. We derive upper and lower bounds on the capacity that coincide in a number...
A jump-diffusion log-return process with log-normal jump amplitudes is presented. The probability density and other properties of the theoretical model are rigorously derived. This theoretical density is fit to empirical log-returns of Standard & Poor’s 500 stock index data. The model repairs some failures found from the log-normal distribution of geometric Brownian motion to model features of...
Computational methods for optimal stopping problems are presented. The first method to be described is based on a linear programming approach to exit time problems of Markov processes and is applicable whenever the objective function is a unimodal function of a threshhold parameter which specifies a stopping time. The second method, using linear and non-linear programming techniques, is a modification...
We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modeled via an underlying Markov process, and under general assumptions, the following results are obtained: (i)Stability of an associated ODE implies that the stochastic recursion is stable in a strong sense when a gain parameter is small.(ii)The range of gain-values...
Motivated by the resurgent interest in efficient adaptive signal processing algorithms for interference suppression in wireless CDMA (Code Division Multiple Access) communication networks, this paper is concerned with asymptotic properties of adaptive filtering algorithms. Our focus is on improving efficiency of sign-regressor procedures, which are known to have reduced complexity compared with the...
Some results on Kalman-type filters for nonparametric estimation problems are presented. On-line recursive filters are proposed for an estimation of a signal and it’s derivatives observed in Gaussian white noise and for a regression estimation with equidistant observation design.
We give a brief survey of recent developments in change-point detection and diagnosis and in estimation of parameters that may undergo occasional changes. There is a large variety of detection and estimation procedures widely scattered in the engineering, economics, statistics and biomedical literature. These procedures can be broadly classified as sequential (or on-line) and fixed sample (or off-line)...
The problem of residual evaluation for fault detection in partially observed diffusions is investigated, using the local asymptotic approach, under the small noise asymptotics. The score function (i.e. the gradient of the log-likelihood function) evaluated at the nominal value of the parameter, and suitably normalized, is used as residual. It is proved that this residual is asymptotically Gaussian,...
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