Statistical Inference for Diffusion Type Processes

Decision making in all spheres of activity involves uncertainty. If rational decisions have to be made, they have to be based on the past observations of the phenomenon in question. Data collection, model building and inference from the data collected, validation of the model and refinement of the model are the key steps or building blocks involved in any rational decision making process. Stochastic processes are widely used for model building in the social, physical, engineering, and life sciences as well as in financial economics. Statistical inference for stochastic processes is of great importance from the theoretical as well as from applications point of view in model building. During the past twenty years, there has been a large amount of progress in the study of inferential aspects for continuous as well as discrete time stochastic processes. Diffusion type processes are a large class of continuous time processes which are widely used for stochastic modelling. the book aims to bring together several methods of estimation of parameters involved in such processes when the process is observed continuously over a period of time or when sampled data is available as generally feasible.

1. Diffusion Type Processes 2. Parametric Inference for Diffusion Type Processes from Continuous Paths 3. Parametric Inference for Diffusion Type Processes from Sampled Data 4. Nonparametric Inference for Diffusion Type Processes from Continuous Sample Paths 5. Nonparametric Inference for Diffusion Type Processes from Sampled Data 6. Applications to Stochastic Modeling 7. Numerical Approximation Methods for Stochastic Differential Equations App. A. Uniform Ergodic Theorem App. B. Stochastic Integration and Limit Theorems for Stochastic Integrals App. C. Wavelets App. D. Gronwall-Bellman Type Lemma