Statistical Inference for Fractional Diffusion Processes

Statistical Inference for Fractional Diffusion Processes looks at statistical inference for stochastic processes modeled by stochastic differential equations driven by fractional Brownian motion. Other related processes, such as sequential inference, nonparametric and non parametric inference and parametric estimation are also discussed.§The book will deal with Fractional Diffusion Processes (FDP) in relation to statistical influence for stochastic processes. The books main focus is on parametric and non parametric inference problems for fractional diffusion processes when a complete path of the process over a finite interval is observable.Stochastic processes are widely used for model building in the social, physical, engineering and life sciences as well as in financial economics. In model building, statistical inference for stochastic processes is of great importance from both a theoretical and an applications point of view.§This book deals with Fractional Diffusion Processes and statistical inference for such stochastic processes. The main focus of the book is to consider parametric and nonparametric inference problems for fractional diffusion processes when a complete path of the process over a finite interval is observable.§Key features:§Introduces self-similar processes, fractional Brownian motion and stochastic integration with respect to fractional Brownian motion.§Provides a comprehensive review of statistical inference for processes driven by fractional Brownian motion for modelling long range dependence.§Presents a study of parametric and nonparametric inference problems for the fractional diffusion process.§Discusses the fractional Brownian sheet and infinite dimensional fractional Brownian motion.§Includes recent results and developments in the area of statistical inference of fractional diffusion processes.§Researchers and students working on the statistics of fractional diffusion processes and applied mathematicians and statisticians involved in stochastic process modelling will benefit from this book.