Hybrid Switching Diffusions: Properties and Applications (Stochastic Modelling and Applied Probability)

This book focuses on switching diffusion processes involving both continuous dynamics and discrete events.

The first part, including three chapters, presents basic properties such as Feller and strong Feller, recurrence, and ergodicity. With a brief review of existence and uniqueness of solutions of switching diffusions, basic properties such as recurrence, Feller properties etc. are dealt with.

The second part of the book is devoted to numerical solutions of switching diffusions.

Containing three chapters, the third part focuses on stability. Chapter seven and chapter eight proceed with the stability analysis. The approach is based on Liapunov function methods.

For convenient references, an appendix including a number of mathematical preliminaries are placed at the end of the book. Topics discussed here including Markov chains, martingales, Gaussian processes, diffusions, jump diffusions, and weak convergence methods. Although detailed developments are often omitted, appropriate references are provided for the reader for further reading.