Browsing by Subject "Large deviations"

Now showing 1 - 4 of 4

Open Access
Entropy, invertibility and variational calculus of adapted shifts on Wiener space
(2009) Üstünel, A.S.
In this work we study the necessary and sufficient conditions for a positive random variable whose expectation under the Wiener measure is one, to be represented as the Radon-Nikodym derivative of the image of the Wiener measure under an adapted perturbation of identity with the help of the associated innovation process. We prove that the innovation conjecture holds if and only if the original process is almost surely invertible. We also give variational characterizations of the invertibility of the perturbations of identity and the representability of a positive random variable whose total mass is equal to unity. We prove in particular that an adapted perturbation of identity U = IW + u satisfying the Girsanov theorem, is invertible if and only if the kinetic energy of u is equal to the entropy of the measure induced with the action of U on the Wiener measure μ, in other words U is invertible ifffrac(1, 2) under(∫, W) | u |H 2 d μ = under(∫, W) frac(d U μ, d μ) log frac(d U μ, d μ) d μ . The relations with the Monge-Kantorovitch measure transportation are also studied. An application of these results to a variational problem related to large deviations is also given. © 2009 Elsevier Inc. All rights reserved.
Open Access
Large deviations of probability rank
(IEEE, 2000) Arıkan, Erdal
Consider a pair of random variables (X,Y) with distribution P. The probability rank function is defined so that G(x|y) = 1 for the most probable outcome x conditional on Y = y, G(x|y) = 2 for the second most probable outcome, and so on, resolving ties between elements with equal probabilities arbitrarily. The function G was considered in [1] in the context of finding the unknown outcome of a random experience by asking question of the form 'Is the outcome equal to x?' sequentially until the actual outcome is determined. The primary focus in [1], and the subsequent works [2], [3], was to find tight bounds on the moments E[G(X|Y)θ]. The present work is closely related to these works but focuses more directly on the large deviations properties of the probability rank function.
Open Access
A particle swarm optimization based SAR motion compensation algorithm for target image reconstruction
(IEEE, 2010) Uğur, Salih; Arıkan, Orhan
A new SAR motion compensation algorithm is proposed for robust reconstruction of target images even under large deviations of the platform from intended flight path. Phase error due to flight path deviations is estimated as a solution to an optimization problem in terms of the positions of the reflectivity centers of the target. Particle swarm optimization is used to obtain phase error estimates efficiently. The quality of the reconstructions is demonstrated by using simulation studies. © 2010 IEEE.
Open Access
Worst-case large deviations upper bounds for i.i.d. sequences under ambiguity
(TÜBİTAK, 2018) Pınar, Mustafa Çelebi
An introductory study of large deviations upper bounds from a worst-case perspective under parameter uncertainty (referred to as ambiguity) of the underlying distributions is given. Borrowing ideas from robust optimization, suitable sets of ambiguity are defined for imprecise parameters of underlying distributions. Both univariate and multivariate i.i.d. sequences of random variables are considered. The resulting optimization problems are challenging min–max (or max–min) problems that admit some simplifications and some explicit results, mostly in the case of the normal probability law.