Regularity and Irregularity of Superprocesses with (1 + )-stable Branching Mechanism

This is the only book discussing multifractal properties of densities of stable superprocesses, containing latest achievements while also giving the reader a comprehensive picture of the state of the art in this area. It is a self-contained presentation of regularity properties of stable superprocesses and proofs of main results and can serve as an introductory text for a graduate course. There are many heuristic explanations of technically involved results and proofs and the reader can get a clear intuitive picture behind the results and techniques.

Introduction, main results and discussion. - Stochastic representation for X and description of the approach for determining regularity. - Some simple properties of (2; d; b )-superprocesses. - Analysis of jumps of superprocesses. - Dichotomy for densities. - Pointwise Hölder exponent at a given point: proof of Theorem 1. 3. - Elements of the proof of Theorem 1. 5 and Proposition 1. 6. - A Estimates for the transition kernel of the one-dimensional Brownian motion. - B Probability inequalities for a spectrally positive stable process. - References.