Over the past 20 years, the study of superprocesses has expanded into a major industry and can now be regarded as a central theme in modern probability theory. This book is intended as a rapid introduction to the subject, geared toward graduate students and researchers in stochastic analysis. A variety of different approaches to the superprocesses emerged over the last ten years. Yet no one approach superseded any others. In this book, readers are exposed to a number of different ways of thinking about the processes, and each is used to motivate some key results. The emphasis is on why results are true rather than on rigorous proof. Specific results are given, including extensive references to current literature for their general form.
Superprocesses as diffusion approximations Qualitative behaviour I The Le Gall representation The relationship between our two classes of superprocesses A countable representation Qualitative behaviour II Introducing interactions Superprocesses and partial differential equations Some more interacting models Appendix Bibliography Index of notation Index.