Regularity and Irregularity of Superprocesses with (1 + beta)-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.
 

List of 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.

Summary

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. 

Product details

• Authors: Leoni Mytnik, Leonid Mytnik, Vitali Wachtel
• Assisted by: Vital Wachtel (Editor), Vitali Wachtel (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2017
• EAN: 9783319500843
• ISBN: 978-3-31-950084-3
• No. of pages: 77
• Dimensions: 158 mm x 235 mm x 4 mm
• Weight: 153 g
• Illustrations: VIII, 77 p. 2 illus.
• Series: SpringerBriefs in Probability and Mathematical Statistics; Springer; SpringerBriefs in Probability and Mathematical Statistics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Stochastik, C, Mathematics and Statistics, Probability Theory and Stochastic Processes, Probabilities, Stochastics, Probability Theory