Alexander Kukush's Books

Radiation Risk Estimation

Based on Measurement Error Models

By: Sergii Masiuk,Alexander Kukush,Sergiy Shklyar,Mykola Chepurny,Illya Likhtarov

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Radiation Risk Estimation

Based on Measurement Error Models

By: Sergii Masiuk,Alexander Kukush,Sergiy Shklyar,Mykola Chepurny,Illya Likhtarov

This monograph discusses statistics and risk estimates applied to radiation damage under the presence of measurement errors. The first part covers nonlinear measurement error models, with a particular emphasis on efficiency of regression parameter estimators. In the second part, risk estimation in models with measurement errors is considered. Efficiency of the methods presented is verified using data from radio-epidemiological studies. Contents: Part I - Estimation in regression models with errors in covariates Measurement error models Linear models with classical error Polynomial regression with known variance of classical error Nonlinear and generalized linear models Part II Radiation risk estimation under uncertainty in exposure doses Overview of risk models realized in program package EPICURE Estimation of radiation risk under classical or Berkson multiplicative error in exposure doses Radiation risk estimation for persons exposed by radioiodine as a result of the Chornobyl accident Elements of estimating equations theory Consistency of efficient methods Efficient SIMEX method as a combination of the SIMEX method and the corrected score method Application of regression calibration in the model with additive error in exposure doses

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Page Count

270

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110433664

ISBN 13

9783110433661

Undergraduate Mathematics Competitions (1995–2016)

Taras Shevchenko National University of Kyiv

By: Volodymyr Brayman,Alexander Kukush

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Undergraduate Mathematics Competitions (1995–2016)

Taras Shevchenko National University of Kyiv

By: Volodymyr Brayman,Alexander Kukush

Versatile and comprehensive in content, this book of problems will appeal to students in nearly all areas of mathematics. The text offers original and advanced problems proposed from 1995 to 2016 at the Mathematics Olympiads. Essential for undergraduate students, PhD students, and instructors, the problems in this book vary in difficulty and cover most of the obligatory courses given at the undergraduate level, including calculus, algebra, geometry, discrete mathematics, measure theory, complex analysis, differential equations, and probability theory. Detailed solutions to all of the problems from Part I are supplied in Part II, giving students the ability to check their solutions and observe new and unexpected ideas. Most of the problems in this book are not technical and allow for a short and elegant solution. The problems given are unique and non-standard; solving the problems requires a creative approach as well as a deep understanding of the material. Nearly all of the problems are originally authored by lecturers, PhD students, senior undergraduates, and graduate students of the mechanics and mathematics faculty of Taras Shevchenko National University of Kyiv as well as by many others from Belgium, Canada, Great Britain, Hungary, and the United States.

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Page Count

214

Publisher

Springer

Published Date

ISBN 10

3319586734

ISBN 13

9783319586731

Theory of Stochastic Processes

With Applications to Financial Mathematics and Risk Theory

By: Dmytro Gusak,Alexander Kukush,Alexey Kulik,Yuliya Mishura,Andrey Pilipenko

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Theory of Stochastic Processes

With Applications to Financial Mathematics and Risk Theory

By: Dmytro Gusak,Alexander Kukush,Alexey Kulik,Yuliya Mishura,Andrey Pilipenko

Providing the necessary materials within a theoretical framework, this volume presents stochastic principles and processes, and related areas. Over 1000 exercises illustrate the concepts discussed, including modern approaches to sample paths and optimal stopping.

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Page Count

379

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387878629

ISBN 13

9780387878621

Gaussian Measures in Hilbert Space

Construction and Properties

By: Alexander Kukush

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Gaussian Measures in Hilbert Space

Construction and Properties

By: Alexander Kukush

At the nexus of probability theory, geometry and statistics, a Gaussian measure is constructed on a Hilbert space in two ways: as a product measure and via a characteristic functional based on Minlos-Sazonov theorem. As such, it can be utilized for obtaining results for topological vector spaces. Gaussian Measures contains the proof for Ferniques theorem and its relation to exponential moments in Banach space. Furthermore, the fundamental Feldman-Hájek dichotomy for Gaussian measures in Hilbert space is investigated. Applications in statistics are also outlined. In addition to chapters devoted to measure theory, this book highlights problems related to Gaussian measures in Hilbert and Banach spaces. Borel probability measures are also addressed, with properties of characteristic functionals examined and a proof given based on the classical Banach Steinhaus theorem. Gaussian Measures is suitable for graduate students, plus advanced undergraduate students in mathematics and statistics. It is also of interest to students in related fields from other disciplines. Results are presented as lemmas, theorems and corollaries, while all statements are proven. Each subsection ends with teaching problems, and a separate chapter contains detailed solutions to all the problems. With its student-tested approach, this book is a superb introduction to the theory of Gaussian measures on infinite-dimensional spaces.

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