Catálogo de publicaciones - libros

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 . The boundedness of the estimator process is enforced by a resetting mechanism. Under appropriate technical conditions the estimator sequence converges to with geometric rate almost surely. This result is in striking contrast to classical stochastic approximation theory where the typical convergence rate is . For the proof a discrete-time version of the ODE-method is used and the techniques of [] are extended. A simple variant of noise free-SPSA is applied to extend a direct controller tuning method named Iterative Feedback Tuning (IFT), see []. Using randomization, the number of experiments required to obtain an unbiased estimate of the gradient of the cost function can be reduced significantly for multi-input multi-output systems.

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 of special cases. The capacity is bounded below by that of the MIMO channel with an additional on-off keying (OOK) transmitter constraint, and it is bounded above by that of parallel, independent multiple-input, single-output (MISO) channels.

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 realistic financial instruments: (1) No large jumps or extreme outliers, (2) Not negatively skewed such that the negative tail is thicker than the positive tail, and (3) Non-leptokurtic due to the lack of thicker tails and higher mode.

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 of a general linear programming approach to optimal stopping problems recently proposed by S. Röhl. Both methods are illustrated by solving Shiryaev’s quickest detection problem for Brownian motion.

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: All results are obtained within the natural operator-theoretic framework of geometrically ergodic Markov processes.

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 usual LMS algorithms and better performance compared with the sign-error procedures. In view of the recent developments in iterate averaging for stochastic approximation methods, algorithms that include both iterate and observation averaging are suggested. It is shown that such algorithms converge to the true parameter and the convergence rate is optimal.

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). We focus on detection and estimation procedures that strike a suitable balance between computational complexity and statistical efficiency, and present some of their asymptotically optimal properties.

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, with mean zero under the null hypothesis, with a different mean (depending linearly on the parameter change) and the same covariance matrix under the contiguous alternative hypothesis. This result relies on the local asymptotic normality (LAN) property for the family of probability distributions of the observation process, which is also proved.

This paper presents a continuous time stochastic adaptive control algorithm for completely observed linear stochastic systems with unknown parameters. The adaptive estimation algorithm is designed so that, first, it drives the estimate into a neighbourhood of a set of parameters corresponding to the true closed loop dynamics and then, second, by activating a performance monitoring feature in , the estimate converges to the true system parameter and the resulting control yields optimal long run LQ closed loop performance.