Regularity and Irregularity of Superprocesses with (1 + β)-stable Branching Mechanism (Springerbriefs in Probability and Mathematical Statistics)

Mytnik, Leonid/ Wachtel, Vitali

Springer International Publishing AG（2017/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 77 p.
• 商品コード 9783319500843

Full Description

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.

 

Contents

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.