ON THE BOUNDARY OF THE SUPPORT OF SUPER-BROWNIAN MOTION

被引：6

作者：

Mueller, Carl ^{[1
]}

Mytnik, Leonid ^{[2
]}

Perkins, Edwin ^{[3
]}

机构：

[1] Univ Rochester, Dept Math, Rochester, NY 14627 USA

[2] Technion Israel Inst Technol, Fac Ind Engn & Management, IL-32000 Haifa, Israel

[3] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

来源：

ANNALS OF PROBABILITY | 2017年 / 45卷 / 6A期

基金：

以色列科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

Super-Brownian motion; Hausdorff dimension; stochastic partial differential equations; HEAT-EQUATION; POTENTIAL-THEORY; SUBORDINATORS; NONUNIQUENESS; COEFFICIENTS; ABSORPTION; UNIQUENESS; NOISE;

D O I：

10.1214/16-AOP1141

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 down arrow 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.

引用

页码：3481 / 3534

页数：54

共 21 条

[1]

[Anonymous], 1955, FUNCTIONAL ANAL

[2]

[Anonymous], 2002, Lecture Notes in Mathematics

[3]

BREZIS H, 1986, ARCH RATION MECH AN, V95, P185, DOI 10.1007/BF00251357

[4] PATHWISE NONUNIQUENESS FOR THE SPDES OF SOME SUPER-BROWNIAN MOTIONS WITH IMMIGRATION [J].

Chen, Yu-Ting .

ANNALS OF PROBABILITY, 2015, 43 (06) :3359-3467

[5]

Coddington E. A., 1955, THEORY ORDINARY DIFF

[6]

DAWSON DA, 1991, MEM AM MATH SOC, V93, pR4

[7] DOMINATED VARIATION AND RELATED CONCEPTS AND TAUBERIAN-THEOREMS FOR LAPLACE TRANSFORMS [J].

DEHAAN, L ;

STADTMULLER, U .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1985, 108 (02) :344-365

[8] LOWER FUNCTIONS FOR INCREASING RANDOM WALKS AND SUBORDINATORS [J].

FRISTEDT, BE ;

PRUITT, WR .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1971, 18 (03) :167-&

[9] POTENTIAL THEORY OF SUBORDINATORS [J].

HAWKES, J .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1975, 33 (02) :113-132

[10]

HAWKES J, 1979, P LOND MATH SOC, V38, P335

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