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

• Main Authors: Mytnik, Leonid (Author), Wachtel, Vitali (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: SpringerBriefs in Probability and Mathematical Statistics,
• Subjects: Mathematics.; Probabilities.; Probability Theory and Stochastic Processes.

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 superproces...

Table 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.