On the boundary of the support of super-brownian notion

Carl Mueller; Leonid Mytnik; Edwin Perkins

doi:10.1214/16-AOP1141

On the boundary of the support of super-brownian notion

Carl Mueller, Leonid Mytnik, Edwin Perkins

Data and Decision Sciences

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

Abstract

We study the density X(t, x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of P(0 < X(t,x) ≤ a) as a ↓ 0 as well as the Hausdorff dimension of the boundary of the support of X(t, ·). The answers are in terms of the leading eigenvalue of the Ornstein-Uhlenbeck generator with a particular killing term. This work is motivated in part by questions of pathwise uniqueness for associated stochastic partial differential equations.

Original language	English
Pages (from-to)	3481-3534
Number of pages	54
Journal	Annals of Probability
Volume	45
Issue number	6
DOIs	https://doi.org/10.1214/16-AOP1141
State	Published - 1 Nov 2017

Keywords

Hausdorff dimension
Stochastic partial differential equations
Super-Brownian motion

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1214/16-AOP1141

Cite this

@article{963be41ccb3d4b85b444e248da213aa3,

title = "On the boundary of the support of super-brownian notion",

abstract = "We study the density X(t, x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of P(0 < X(t,x) ≤ a) as a ↓ 0 as well as the Hausdorff dimension of the boundary of the support of X(t, ·). The answers are in terms of the leading eigenvalue of the Ornstein-Uhlenbeck generator with a particular killing term. This work is motivated in part by questions of pathwise uniqueness for associated stochastic partial differential equations.",

keywords = "Hausdorff dimension, Stochastic partial differential equations, Super-Brownian motion",

author = "Carl Mueller and Leonid Mytnik and Edwin Perkins",

note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2017.",

year = "2017",

month = nov,

day = "1",

doi = "10.1214/16-AOP1141",

language = "אנגלית",

volume = "45",

pages = "3481--3534",

number = "6",

}

TY - JOUR

T1 - On the boundary of the support of super-brownian notion

AU - Mueller, Carl

AU - Mytnik, Leonid

AU - Perkins, Edwin

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2017.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - We study the density X(t, x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of P(0 < X(t,x) ≤ a) as a ↓ 0 as well as the Hausdorff dimension of the boundary of the support of X(t, ·). The answers are in terms of the leading eigenvalue of the Ornstein-Uhlenbeck generator with a particular killing term. This work is motivated in part by questions of pathwise uniqueness for associated stochastic partial differential equations.

AB - We study the density X(t, x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of P(0 < X(t,x) ≤ a) as a ↓ 0 as well as the Hausdorff dimension of the boundary of the support of X(t, ·). The answers are in terms of the leading eigenvalue of the Ornstein-Uhlenbeck generator with a particular killing term. This work is motivated in part by questions of pathwise uniqueness for associated stochastic partial differential equations.

KW - Hausdorff dimension

KW - Stochastic partial differential equations

KW - Super-Brownian motion

UR - http://www.scopus.com/inward/record.url?scp=85035116562&partnerID=8YFLogxK

U2 - 10.1214/16-AOP1141

DO - 10.1214/16-AOP1141

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

AN - SCOPUS:85035116562

SN - 0091-1798

VL - 45

SP - 3481

EP - 3534

JO - Annals of Probability

JF - Annals of Probability

IS - 6

ER -

On the boundary of the support of super-brownian notion

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this