Regularity and irregularity of superprocesses with (1 + β)-stable branching mechanism / by Leonid Mytnik, Vitali Wachtel.

Format:

Book

Author/Creator:

Mytnik, Leonid., Author.

Wachtel, Vitali., Author.

Series:

SpringerBriefs in Probability and Mathematical Statistics, 2365-4333

Language:

English

Subjects (All):

Probabilities.

Probability Theory and Stochastic Processes.

Local Subjects:

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (80 pages).

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

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. .

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.

Notes:

Includes bibliographical references and index.