Simulation of Stochastic Processes with Given Accuracy and Reliability

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.

Autorentext

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 TechnologyMain 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 -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.

Inhalt

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.