Results 1 to 10 of about 590,794 (165)
Random Variables and Stable Distributions on Fractal Cantor Sets
Fractal and Fractional, 2019 In this paper, we introduce the concept of fractal random variables and their related distribution functions and statistical properties. Fractal calculus is a generalisation of standard calculus which includes function with fractal support.
Alireza Khalili Golmankhaneh +1 more
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Bernoulli Filters for Multiple Correlated Sensors
IEEE Access, 2021 The Bernoulli filter is a general, Bayes-optimal solution for tracking a single disappearing and reappearing target, using a single sensor whose observations are corrupted by missed detections and a general, known clutter process.
Ronald Mahler
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Bayes-Optimal Set-Valued Tracking of Single Point Targets
IEEE Access, 2021 Conventional single-point-target tracking algorithms are recursive point estimators with point-measurement input data. In less well-known approaches, the tracking algorithm is a recursive set estimator with point-measurement or set-measurement input data.
Ronald Paxton-Sheets Mahler
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Intersections of random sets [PDF]
Journal of Applied Probability, 2022 AbstractWe consider a variant of a classical coverage process, the Boolean model in$\mathbb{R}^d$. Previous efforts have focused on convergence of the unoccupied region containing the origin to a well-studied limitC. We study the intersection of sets centered at points of a Poisson point process confined to the unit ball.
Jacob Richey, Amites Sarkar
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Bayes‐optimal tracking of two statistically correlated targets in general clutter
IET Signal Processing, 2022 The Bernoulli filter is a very general, computationally feasible Bayes‐optimal approach for tracking a single disappearing and reappearing target, using a single sensor whose observations are corrupted by missed detections and a known, general point ...
Ronald Mahler
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Set-Valued T-Translative Functions and Their Applications in Finance
Mathematics, 2021 A theory for set-valued functions is developed, which are translative with respect to a linear operator. It is shown that such functions cover a wide range of applications, from projections in Hilbert spaces, set-valued quantiles for vector-valued random
Andreas H. Hamel, Frank Heyde
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The Pairwise-Markov Bernoulli Filter
IEEE Access, 2020 The Bernoulli filter is a general, Bayes-optimal solution for tracking a single disappearing and reappearing target, using a sensor whose observations are corrupted by missed detections and a general, known clutter process.
Ronald Mahler
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Advances in Applied Probability, 2012 We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite.
Ballani, F. +2 more
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Random Sampling Many-Dimensional Sets Arising in Control
Mathematics, 2021 Various Monte Carlo techniques for random point generation over sets of interest are widely used in many areas of computational mathematics, optimization, data processing, etc.
Pavel Shcherbakov +2 more
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Boolean Valued Representation of Random Sets and Markov Kernels with Application to Large Deviations
Mathematics, 2020 We establish a connection between random set theory and Boolean valued analysis by showing that random Borel sets, random Borel functions, and Markov kernels are respectively represented by Borel sets, Borel functions, and Borel probability measures in a
Antonio Avilés López +1 more
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