Estimation Of Stochastic Processes With Stationary Increments And Cointegrated Sequences
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Estimation Of Stochastic Processes With Stationary Increments And Cointegrated Sequences
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Author : Maksym Luz
language : en
Publisher: John Wiley & Sons
Release Date : 2019-09-25
Estimation Of Stochastic Processes With Stationary Increments And Cointegrated Sequences written by Maksym Luz and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-25 with Mathematics categories.
Estimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences. Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.
Estimation Of Stochastic Processes With Stationary Increments And Cointegrated Sequences
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Author : Maksym Luz
language : en
Publisher: John Wiley & Sons
Release Date : 2019-09-20
Estimation Of Stochastic Processes With Stationary Increments And Cointegrated Sequences written by Maksym Luz and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-20 with Mathematics categories.
Estimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences. Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.
Non Stationary Stochastic Processes Estimation
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Author : Maksym Luz
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-05-20
Non Stationary Stochastic Processes Estimation written by Maksym Luz and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-20 with Business & Economics categories.
The problem of forecasting future values of economic and physical processes, the problem of restoring lost information, cleaning signals or other data observations from noise, is magnified in an information-laden word. Methods of stochastic processes estimation depend on two main factors. The first factor is construction of a model of the process being investigated. The second factor is the available information about the structure of the process under consideration. In this book, we propose results of the investigation of the problem of mean square optimal estimation (extrapolation, interpolation, and filtering) of linear functionals depending on unobserved values of stochastic sequences and processes with periodically stationary and long memory multiplicative seasonal increments. Formulas for calculating the mean square errors and the spectral characteristics of the optimal estimates of the functionals are derived in the case of spectral certainty, where spectral structure of the considered sequences and processes are exactly known. In the case where spectral densities of the sequences and processes are not known exactly while some sets of admissible spectral densities are given, we apply the minimax-robust method of estimation.
International Encyclopedia Of Statistical Science
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Author : Miodrag Lovric
language : en
Publisher: Springer Nature
Release Date : 2025-06-19
International Encyclopedia Of Statistical Science written by Miodrag Lovric and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.
The International Encyclopedia of Statistical Science stands as a monumental effort to enrich statistics education globally, particularly in regions facing educational challenges. By amalgamating the expertise of over 700 authors from 110 countries, including Nobel Laureates and presidents of statistical societies, it offers an unparalleled resource for readers worldwide. This encyclopedia is not just a collection of entries; it is a concerted effort to revive statistics as a vibrant, critical field of study and application. Providing a comprehensive and accessible account of statistical terms, methods, and applications, it enables readers to gain a quick insight into the subject, regardless of their background. This work serves to refresh and expand the knowledge of researchers, managers, and practitioners, highlighting the relevance and applicability of statistics across various fields, from economics and business to healthcare and public policy. Furthermore, it aims to inspire students by demonstrating the significance of statistics in solving real-world problems, thus encouraging a new generation to explore and contribute to the field.
Asymptotic And Analytic Methods In Stochastic Evolutionary Symptoms
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Author : Dmitri Koroliouk
language : en
Publisher: John Wiley & Sons
Release Date : 2023-08-29
Asymptotic And Analytic Methods In Stochastic Evolutionary Symptoms written by Dmitri Koroliouk and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-29 with Mathematics categories.
This book illustrates a number of asymptotic and analytic approaches applied for the study of random evolutionary systems, and considers typical problems for specific examples. In this case, constructive mathematical models of natural processes are used, which more realistically describe the trajectories of diffusion-type processes, rather than those of the Wiener process. We examine models where particles have some free distance between two consecutive collisions. At the same time, we investigate two cases: the Markov evolutionary system, where the time during which the particle moves towards some direction is distributed exponentially with intensity parameter λ; and the semi-Markov evolutionary system, with arbitrary distribution of the switching process. Thus, the models investigated here describe the motion of particles with a finite speed and the proposed random evolutionary process with characteristics of a natural physical process: free run and finite propagation speed. In the proposed models, the number of possible directions of evolution can be finite or infinite.
Random Motions In Markov And Semi Markov Random Environments 2
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Author : Anatoliy Pogorui
language : en
Publisher: John Wiley & Sons
Release Date : 2021-01-11
Random Motions In Markov And Semi Markov Random Environments 2 written by Anatoliy Pogorui and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-11 with Mathematics categories.
This book is the second of two volumes on random motions in Markov and semi-Markov random environments. This second volume focuses on high-dimensional random motions. This volume consists of two parts. The first expands many of the results found in Volume 1 to higher dimensions. It presents new results on the random motion of the realistic three-dimensional case, which has so far been barely mentioned in the literature, and deals with the interaction of particles in Markov and semi-Markov media, which has, in contrast, been a topic of intense study. The second part contains applications of Markov and semi-Markov motions in mathematical finance. It includes applications of telegraph processes in modeling stock price dynamics and investigates the pricing of variance, volatility, covariance and correlation swaps with Markov volatility and the same pricing swaps with semi-Markov volatilities.
Random Motions In Markov And Semi Markov Random Environments 1
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Author : Anatoliy Pogorui
language : en
Publisher: John Wiley & Sons
Release Date : 2021-03-16
Random Motions In Markov And Semi Markov Random Environments 1 written by Anatoliy Pogorui and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-16 with Mathematics categories.
This book is the first of two volumes on random motions in Markov and semi-Markov random environments. This first volume focuses on homogenous random motions. This volume consists of two parts, the first describing the basic concepts and methods that have been developed for random evolutions. These methods are the foundational tools used in both volumes, and this description includes many results in potential operators. Some techniques to find closed-form expressions in relevant applications are also presented. The second part deals with asymptotic results and presents a variety of applications, including random motion with different types of boundaries, the reliability of storage systems and solutions of partial differential equations with constant coefficients, using commutative algebra techniques. It also presents an alternative formulation to the Black-Scholes formula in finance, fading evolutions and telegraph processes, including jump telegraph processes and the estimation of the number of level crossings for telegraph processes.
General Stochastic Measures
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Author : Vadym M. Radchenko
language : en
Publisher: John Wiley & Sons
Release Date : 2022-09-21
General Stochastic Measures written by Vadym M. Radchenko and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-21 with Mathematics categories.
This book is devoted to the study of stochastic measures (SMs). An SM is a sigma-additive in probability random function, defined on a sigma-algebra of sets. SMs can be generated by the increments of random processes from many important classes such as square-integrable martingales and fractional Brownian motion, as well as alpha-stable processes. SMs include many well-known stochastic integrators as partial cases. General Stochastic Measures provides a comprehensive theoretical overview of SMs, including the basic properties of the integrals of real functions with respect to SMs. A number of results concerning the Besov regularity of SMs are presented, along with equations driven by SMs, types of solution approximation and the averaging principle. Integrals in the Hilbert space and symmetric integrals of random functions are also addressed. The results from this book are applicable to a wide range of stochastic processes, making it a useful reference text for researchers and postgraduate or postdoctoral students who specialize in stochastic analysis.
Stochastic Modeling And Optimization Methods For Critical Infrastructure Protection Volume 2
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Author : Alexei A. Gaivoronski
language : en
Publisher: John Wiley & Sons
Release Date : 2025-04-29
Stochastic Modeling And Optimization Methods For Critical Infrastructure Protection Volume 2 written by Alexei A. Gaivoronski and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-29 with Business & Economics categories.
Stochastic Modeling and Optimization Methods for Critical Infrastructure Protection is a thorough exploration of mathematical models and tools that are designed to strengthen critical infrastructures against threats – both natural and adversarial. Divided into two volumes, this first volume examines stochastic modeling across key economic sectors and their interconnections, while the second volume focuses on advanced mathematical methods for enhancing infrastructure protection. The book covers a range of themes, including risk assessment techniques that account for systemic interdependencies within modern technospheres, the dynamics of uncertainty, instability and system vulnerabilities. The book also presents other topics such as cryptographic information protection and Shannon’s theory of secret systems, alongside solutions arising from optimization, game theory and machine learning approaches. Featuring research from international collaborations, this book covers both theory and applications, offering vital insights for advanced risk management curricula. It is intended not only for researchers, but also educators and professionals in infrastructure protection and stochastic optimization.
Stochastic Modeling And Optimization Methods For Critical Infrastructure Protection Volume 2
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Author : Alexei A. Gaivoronski
language : en
Publisher: John Wiley & Sons
Release Date : 2025-05-13
Stochastic Modeling And Optimization Methods For Critical Infrastructure Protection Volume 2 written by Alexei A. Gaivoronski and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-13 with Business & Economics categories.
Stochastic Modeling and Optimization Methods for Critical Infrastructure Protection is a thorough exploration of mathematical models and tools that are designed to strengthen critical infrastructures against threats – both natural and adversarial. Divided into two volumes, this first volume examines stochastic modeling across key economic sectors and their interconnections, while the second volume focuses on advanced mathematical methods for enhancing infrastructure protection. The book covers a range of themes, including risk assessment techniques that account for systemic interdependencies within modern technospheres, the dynamics of uncertainty, instability and system vulnerabilities. The book also presents other topics such as cryptographic information protection and Shannon’s theory of secret systems, alongside solutions arising from optimization, game theory and machine learning approaches. Featuring research from international collaborations, this book covers both theory and applications, offering vital insights for advanced risk management curricula. It is intended not only for researchers, but also educators and professionals in infrastructure protection and stochastic optimization.