Simulation of Stochastic Processes with Given Accuracy and Reliability

ISBN-13: 9781785482175 / Angielski / Twarda / 2016 / 346 str.

Yuriy V. Kozachenko; Oleksandr O. Pogorilyak; Iryna V. Rozora

Opis

Simulation has now become an integral part of research and development across many fields of study. Despite the large amounts of literature in the field of simulation and modeling, one recurring problem is the issue of accuracy and confidence level of constructed models. By outlining the new approaches and modern methods of simulation of stochastic processes, this book provides methods and tools in measuring accuracy and reliability in functional spaces. The authors explore analysis of the theory of Sub-Gaussian (including Gaussian one) and Square Gaussian random variables and processes and Cox processes. Methods of simulation of stochastic processes and fields with given accuracy and reliability in some Banach spaces are also considered.

• Provides an analysis of the theory of Sub-Gaussian (including Gaussian one) and Square Gaussian random variables and processes
• Contains information on the study of the issue of accuracy and confidence level of constructed models not found in other books on the topic
• Provides methods and tools in measuring accuracy and reliability in functional spaces

Recenzje

"The book will be useful both for mathematicians and practitioners who deal with stochastic models. It contains rigorous formulas together with simulation results. The mathematical level of the book is high, however it is accessible for everybody who is interested in approximations of stochastic processes." --Zentralblatt MATH 1376

Spis treści

1. The Distribution of the Estimates for the Norm of Sub-Gaussian Stochastic Processes.
2. Simulation of Stochastic Processes Presented in the Form of Series.
3. Simulation of Gaussian Stochastic Processes with Respect to Output Processes of the System.
4. The Construction of the Model of Gaussian Stationary Processes.
5. The Modeling of Gaussian Stationary Random?Processes with a Certain Accuracy and Reliability.
6. Simulation of Cox Random Processes.
7. On the Modeling of Gaussian Stationary Processes with Absolutely Continuous Spectrum.
8. Simulation of Gaussian Isotropic Random Fields on a Sphere.

O autorze

Yuriy Kozachenko is Professor at Taras Shevchenko National University of Kyiv, Ukraine.Doctor of Sciences in Physics and Mathematics, Laureate of the State Prize of Ukraine in Science and Technology

Main scientific research interests relate to the study of the properties of random processes in various functional spaces, simulation and statistics of random processes, the theory of wavelet expansions of random processes. One of the founders of the theory of sub-Gaussian and f-subGaussian random processes, random processes from Orlicz spaces. Determination of accuracy and reliability of computer simulation of random processes.

Author of over 300 scientific papers, several textbooks and seven monographs.

Associate professor at Department of Department of Probability Theory and Mathematical Analysis, UzhNU from 2008;

Her scientific interests are in the field of simulation of point stochastic processes and fields with given accuracy and reliability, e.g. Cox Processes driven by random intensity, analytical properties of point processes and fields. Author of more than 10 papers.

Associate professor at Department of Applied Statistics, TSNUK, Ukraine from 2011.

Her scientific interests are in the field of simulation of stochastic processes and fields with given accuracy and reliability in different Banach spaces, analytical properties of stochastic processes and fields; survey statistics. Author of more than 40 papers.

Associate professor at Department of Applied Statistics, from 2011.Her scientific interests are in the field of simulation of stochastic processes and fields with given accuracy and reliability in different Banach spaces, analytical properties of stochastic processes and fields; survey statistics. Author of more than 20 papers