On the Pathwise Uniqueness of Solutions of One-Dimensional Stochastic Differential Equations with Jumps

被引：1

作者：

Benabdallah, Mohsine ^{[1
]}

Bouhadou, Siham ^{[2
]}

Ouknine, Youssef ^{[2
]}

机构：

[1] Ibn Tofail Univ, Dept Math, BP 133, Kenitra, Morocco

[2] Cadi Ayyad Univ, Fac Sci Semlalia, Dept Math, LIBMA Lab, PBO 2390, Marrakech, Morocco

来源：

STATISTICAL METHODS AND APPLICATIONS IN INSURANCE AND FINANCE | 2016年 / 158卷

关键词：

Semimartingale; Local time; Tanaka formula; Pathwise uniqueness; LOCAL-TIMES;

D O I：

10.1007/978-3-319-30417-5_8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider one-dimensional stochastic differential equations with jumps in the general case. We introduce new technics based on local time and we prove newresults on pathwise uniqueness and comparison theorems. Our approach are very easy to handled. Similar equations without jumps were studied in the same context by [10, 15] and others authors.

引用

页码：193 / 210

页数：18

共 50 条

[31] One-dimensional stochastic differential equations with generalized and singular drift
Blei, Stefan
Engelbert, Hans-Juergen
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (12) : 4337 - 4372
[32] On pathwise uniqueness of stochastic evolution equations in Hilbert spaces
Bin Xie
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 344 (01) : 204 - 216
[33] ON A STRONG UNIQUENESS OF SOLUTIONS OF DEGENERATE STOCHASTIC DIFFERENTIAL EQUATIONS
Shaposhnikov, A. V.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2012, 56 (02) : 240 - 251
[34] The uniqueness of solutions of perturbed backward stochastic differential equations
Constantin, G
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 300 (01) : 12 - 16
[35] 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
[36] Limit theorem for one-dimensional stochastic equations
Makhno, SY
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2003, 48 (01) : 164 - 169
[37] Pathwise uniqueness for singular stochastic Volterra equations with Hölder coefficients
Proemel, David J.
Scheffels, David
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2025, 13 (01): : 308 - 366
[38] Existence and uniqueness of solutions for perturbed stochastic differential equations with reflected boundary
Bahaj, Faiz
Hiderah, Kamal
MONTE CARLO METHODS AND APPLICATIONS, 2024, 30 (01): : 31 - 41
[39] Regularisation by fractional noise for one-dimensional differential equations with distributional drift
Anzeletti, Lukas
Richard, Alexandre
Tanre, Etienne
ELECTRONIC JOURNAL OF PROBABILITY, 2023, 28
[40] Absolute continuity of the laws of one-dimensional reflected stochastic differential equations involving the maximum process
Zhang, Hua
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 495 (01)

← 1 2 3 4 5 →