Regularity and Irregularity of Superprocesses with (1 + β)-stable Branching Mechanism [electronic resource] / by Leonid Mytnik, Vitali Wachtel.

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.

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. .