Almost Periodic Stochastic Processes
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Almost Periodic Stochastic Processes
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Author : Paul H. Bezandry
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-07
Almost Periodic Stochastic Processes written by Paul H. Bezandry and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-07 with Mathematics categories.
This book lays the foundations for a theory on almost periodic stochastic processes and their applications to various stochastic differential equations, functional differential equations with delay, partial differential equations, and difference equations. It is in part a sequel of authors recent work on almost periodic stochastic difference and differential equations and has the particularity to be the first book that is entirely devoted to almost periodic random processes and their applications. The topics treated in it range from existence, uniqueness, and stability of solutions for abstract stochastic difference and differential equations.
Almost Periodicity And Almost Automorphy
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Author : Abdallah Afoukal
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-03
Almost Periodicity And Almost Automorphy written by Abdallah Afoukal 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 2025-03-03 with Mathematics categories.
When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an “ordinary differential equation” with respect to the variable which was put in evidence. Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems. Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.
Fourier Analysis Of Economic Phenomena
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Author : Toru Maruyama
language : en
Publisher: Springer
Release Date : 2019-07-03
Fourier Analysis Of Economic Phenomena written by Toru Maruyama and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-03 with Mathematics categories.
This is the first monograph that discusses in detail the interactions between Fourier analysis and dynamic economic theories, in particular, business cycles.Many economic theories have analyzed cyclical behaviors of economic variables. In this book, the focus is on a couple of trials: (1) the Kaldor theory and (2) the Slutsky effect. The Kaldor theory tries to explain business fluctuations in terms of nonlinear, 2nd-order ordinary differential equations (ODEs). In order to explain periodic behaviors of a solution, the Hopf-bifurcation theorem frequently plays a key role. Slutsky's idea is to look at the periodic movement as an overlapping effect of random shocks. The Slutsky process is a weakly stationary process, the periodic (or almost periodic) behavior of which can be analyzed by the Bochner theorem. The goal of this book is to give a comprehensive and rigorous justification of these ideas. Therefore, the aim is first to give a complete theory that supports the Hopftheorem and to prove the existence of periodic solutions of ODEs; and second to explain the mathematical structure of the Bochner theorem and its relation to periodic (or almost periodic) behaviors of weakly stationary processes.Although these two targets are the principal ones, a large number of results from Fourier analysis must be prepared in order to reach these goals. The basic concepts and results from classical as well as generalized Fourier analysis are provided in a systematic way.Prospective readers are assumed to have sufficient knowledge of real, complex analysis. However, necessary economic concepts are explained in the text, making this book accessible even to readers without a background in economics.
Combined Measure And Shift Invariance Theory Of Time Scales And Applications
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Author : Chao Wang
language : en
Publisher: Springer Nature
Release Date : 2022-09-22
Combined Measure And Shift Invariance Theory Of Time Scales And Applications written by Chao Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-22 with Mathematics categories.
This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales. First proposed by S. Hilger, the time scale theory—a unified view of continuous and discrete analysis—has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains. As a new and exciting type of mathematics—and more comprehensive and versatile than the traditional theories of differential and difference equations—, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences. Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.
Stochastic Processes And Functional Analysis
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Author : Alan C. Krinik
language : en
Publisher: CRC Press
Release Date : 2004-03-23
Stochastic Processes And Functional Analysis written by Alan C. Krinik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-23 with Mathematics categories.
This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochas
Long Range Dependent Processes Theory And Applications
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Author : Ming Li
language : en
Publisher: Frontiers Media SA
Release Date : 2022-12-05
Long Range Dependent Processes Theory And Applications written by Ming Li and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-05 with Science categories.
Cyclostationary Processes And Time Series
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Author : Antonio Napolitano
language : en
Publisher: Academic Press
Release Date : 2019-10-24
Cyclostationary Processes And Time Series written by Antonio Napolitano and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-24 with Technology & Engineering categories.
Many processes in nature arise from the interaction of periodic phenomena with random phenomena. The results are processes that are not periodic, but whose statistical functions are periodic functions of time. These processes are called cyclostationary and are an appropriate mathematical model for signals encountered in many fields including communications, radar, sonar, telemetry, acoustics, mechanics, econometrics, astronomy, and biology. Cyclostationary Processes and Time Series: Theory, Applications, and Generalizations addresses these issues and includes the following key features. - Presents the foundations and developments of the second- and higher-order theory of cyclostationary signals - Performs signal analysis using both the classical stochastic process approach and the functional approach for time series - Provides applications in signal detection and estimation, filtering, parameter estimation, source location, modulation format classification, and biological signal characterization - Includes algorithms for cyclic spectral analysis along with Matlab/Octave code - Provides generalizations of the classical cyclostationary model in order to account for relative motion between transmitter and receiver and describe irregular statistical cyclicity in the data
Semilinear Evolution Equations And Their Applications
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Author : Toka Diagana
language : en
Publisher: Springer
Release Date : 2018-10-23
Semilinear Evolution Equations And Their Applications written by Toka Diagana and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-23 with Mathematics categories.
This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including degenerate ones. Various stability, uniqueness, and existence results are established using various tools from nonlinear functional analysis and operator theory (such as semigroup methods). Various applications to partial differential equations and the dynamic of populations are amply discussed. This self-contained volume is primarily intended for advanced undergraduate and graduate students, post-graduates and researchers, but may also be of interest to non-mathematicians such as physicists and theoretically oriented engineers. It can also be used as a graduate text on evolution equations and difference equations and their applications to partial differential equations and practical problems arising in population dynamics. For completeness, detailed preliminary background on Banach and Hilbert spaces, operator theory, semigroups of operators, and almost periodic functions and their spectral theory are included as well.
Nonlinear Analysis Geometry And Applications
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Author : Diaraf Seck
language : en
Publisher: Springer Nature
Release Date : 2024-05-22
Nonlinear Analysis Geometry And Applications written by Diaraf Seck and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-22 with Mathematics categories.
The NLAGA's Biennial International Research Symposium (NLAGA-BIRS) is intended to gather African expertises in Nonlinear Analysis, Geometry and their Applications with their international partners in a four days conference where new mathematical results are presented and discussed. This book features the best papers presented during this Biennial. The different topics addressed are related to Partial Differential Equations, Differential inclusions, Geometrical Analysis of Optimal Shapes, Complex Analysis, Geometric Structures, Algebraic Geometry, Algebraic, Optimization, Optimal Control and Mathematical modeling. The main focus of the NLAGA project is to deepen and consolidate the development in West and Center Africa of Nonlinear Analysis, Geometry and their Applications, aimed at solving in particular real-world problems such as coastal erosion, urban network, pollution problems, and population dynamics.
Generalizations Of Cyclostationary Signal Processing
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Author : Antonio Napolitano
language : en
Publisher: John Wiley & Sons
Release Date : 2012-12-07
Generalizations Of Cyclostationary Signal Processing written by Antonio Napolitano 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 2012-12-07 with Technology & Engineering categories.
The relative motion between the transmitter and the receiver modifies the nonstationarity properties of the transmitted signal. In particular, the almost-cyclostationarity property exhibited by almost all modulated signals adopted in communications, radar, sonar, and telemetry can be transformed into more general kinds of nonstationarity. A proper statistical characterization of the received signal allows for the design of signal processing algorithms for detection, estimation, and classification that significantly outperform algorithms based on classical descriptions of signals.Generalizations of Cyclostationary Signal Processing addresses these issues and includes the following key features: Presents the underlying theoretical framework, accompanied by details of their practical application, for the mathematical models of generalized almost-cyclostationary processes and spectrally correlated processes; two classes of signals finding growing importance in areas such as mobile communications, radar and sonar. Explains second- and higher-order characterization of nonstationary stochastic processes in time and frequency domains. Discusses continuous- and discrete-time estimators of statistical functions of generalized almost-cyclostationary processes and spectrally correlated processes. Provides analysis of mean-square consistency and asymptotic Normality of statistical function estimators. Offers extensive analysis of Doppler channels owing to the relative motion between transmitter and receiver and/or surrounding scatterers. Performs signal analysis using both the classical stochastic-process approach and the functional approach, where statistical functions are built starting from a single function of time.