Optimal local Hölder index for density states of superprocesses with (1 +β)-branching mechanism

Klaus Fleischmann; Leonid Mytnik; Vitali Wachtel

doi:10.1214/09-AOP501

Optimal local Hölder index for density states of superprocesses with (1 +β)-branching mechanism

Klaus Fleischmann, Leonid Mytnik, Vitali Wachtel

Data and Decision Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

For 0 <α ≤ 2, a super-α-stable motion X in R^d with branching of index 1 +β ∈ (1, 2) is considered. Fix arbitrary t > 0. If d <α/β, a dichotomy for the density function of the measure Xt holds: the density function is locally Hölder continuous if d = 1 and α >1 + β but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local Hölder index.

Original language	English
Pages (from-to)	1180-1220
Number of pages	41
Journal	Annals of Probability
Volume	38
Issue number	3
DOIs	https://doi.org/10.1214/09-AOP501
State	Published - May 2010

Keywords

Critical index
Dichotomy for density of superprocess states
Hausdorff dimension
Hölder continuity
Local unboundedness
Multifractal spectrum
Optimal exponent

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1214/09-AOP501

Cite this

@article{38215bfcb524476eb923ad251e9646f1,

title = "Optimal local H{\"o}lder index for density states of superprocesses with (1 +β)-branching mechanism",

abstract = "For 0 <α ≤ 2, a super-α-stable motion X in Rd with branching of index 1 +β ∈ (1, 2) is considered. Fix arbitrary t > 0. If d <α/β, a dichotomy for the density function of the measure Xt holds: the density function is locally H{\"o}lder continuous if d = 1 and α >1 + β but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local H{\"o}lder index.",

keywords = "Critical index, Dichotomy for density of superprocess states, Hausdorff dimension, H{\"o}lder continuity, Local unboundedness, Multifractal spectrum, Optimal exponent",

author = "Klaus Fleischmann and Leonid Mytnik and Vitali Wachtel",

year = "2010",

month = may,

doi = "10.1214/09-AOP501",

language = "אנגלית",

volume = "38",

pages = "1180--1220",

number = "3",

}

TY - JOUR

T1 - Optimal local Hölder index for density states of superprocesses with (1 +β)-branching mechanism

AU - Fleischmann, Klaus

AU - Mytnik, Leonid

AU - Wachtel, Vitali

PY - 2010/5

Y1 - 2010/5

N2 - For 0 <α ≤ 2, a super-α-stable motion X in Rd with branching of index 1 +β ∈ (1, 2) is considered. Fix arbitrary t > 0. If d <α/β, a dichotomy for the density function of the measure Xt holds: the density function is locally Hölder continuous if d = 1 and α >1 + β but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local Hölder index.

AB - For 0 <α ≤ 2, a super-α-stable motion X in Rd with branching of index 1 +β ∈ (1, 2) is considered. Fix arbitrary t > 0. If d <α/β, a dichotomy for the density function of the measure Xt holds: the density function is locally Hölder continuous if d = 1 and α >1 + β but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local Hölder index.

KW - Critical index

KW - Dichotomy for density of superprocess states

KW - Hausdorff dimension

KW - Hölder continuity

KW - Local unboundedness

KW - Multifractal spectrum

KW - Optimal exponent

UR - http://www.scopus.com/inward/record.url?scp=77957071990&partnerID=8YFLogxK

U2 - 10.1214/09-AOP501

DO - 10.1214/09-AOP501

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:77957071990

SN - 0091-1798

VL - 38

SP - 1180

EP - 1220

JO - Annals of Probability

JF - Annals of Probability

IS - 3

ER -

Optimal local Hölder index for density states of superprocesses with (1 +β)-branching mechanism

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this