ON THE PATHWISE UNIQUENESS FOR A CLASS OF DEGENERATE ITO-STOCHASTIC DIFFERENTIAL EQUATIONS

被引：0

作者：

Lee, Haesung ^{[1
]}

机构：

[1] Korea Sci Acad KAIST, Dept Math & Comp Sci, Busan 47162, 105-47 Baegyanggwanmun ro, Busan 10547, South Korea

来源：

OSAKA JOURNAL OF MATHEMATICS | 2023年 / 60卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

SDES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show pathwise uniqueness for a class of degenerate Ito-SDE among all of its weak solutions that spend zero time at the points of degeneracy of the dispersion matrix. Consequently, by the Yamada-Watanabe Theorem and a weak existence result, the pathwise unique solutions can be shown to be strong and to exist. The main tools to show pathwise uniqueness are inequalities associated with maximal functions and a Krylov type estimate derived from elliptic regularity and uniqueness in law.

引用

页码：533 / 543

页数：11

共 50 条

[41] Pathwise uniqueness of multi-dimensional stochastic differential equations with Hölder diffusion coefficients
Dejun Luo
Frontiers of Mathematics in China, 2011, 6 : 129 - 136
[42] THE PATHWISE UNIQUENESS OF SOLUTION OF NON-MARKOVIAN STOCHASTIC DIFFERENTIAL-EQUATIONS WITH JUMPS IN PLANE
LONG, HW
CHINESE SCIENCE BULLETIN, 1994, 39 (22): : 1853 - 1858
[43] Existence and pathwise uniqueness of solutions for stochastic differential equations involving the local time at point zero
Hiderah, Kamal
STOCHASTIC ANALYSIS AND APPLICATIONS, 2023, 41 (02) : 276 - 290
[44] Pathwise uniqueness of stochastic differential equations driven by Brownian motions and finite variation Levy processes
Tsukada, Hiroshi
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2022, 94 (01) : 143 - 162
[45] On the pathwise uniqueness of solutions of stochastic differential equations driven by multi-dimensional symmetric α stable
Tsuchiya, Takahiro
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2006, 46 (01): : 107 - 121
[46] ON THE PATHWISE UNIQUENESS OF SOLUTIONS OF ONE-DIMENSIONAL STOCHASTIC DIFFERENTIAL-EQUATIONS OF JUMP TYPE
KOMATSU, T
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1982, 58 (08) : 353 - 356
[47] Existence and Uniqueness of Solutions for a Class of Nonlinear Stochastic Differential Equations
Komashynska, Iryna Volodymyrivna
ABSTRACT AND APPLIED ANALYSIS, 2013,
[48] On degenerate stochastic equations of Ito type with jumps
Kurenok, V. P.
STATISTICS & PROBABILITY LETTERS, 2008, 78 (17) : 2917 - 2925
[49] Strong Solution Existence for a Class of Degenerate Stochastic Differential Equations
McEneaney, William M.
Kaise, Hidehiro
Dower, Peter M.
Zhao, Ruobing
IFAC PAPERSONLINE, 2020, 53 (02): : 2220 - 2224
[50] A (rough) pathwise approach to a class of non-linear stochastic partial differential equations
Caruana, Michael
Friz, Peter K.
Oberhauser, Harald
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2011, 28 (01): : 27 - 46

← 1 2 3 4 5 →