Martingale Nature and Laws of the Iterated Logarithm for Markov Processes of Pure-Jump Type

被引：0

作者：

Shiozawa, Yuichi ^{[1
]}

Wang, Jian ^{[2
]}

机构：

[1] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan

[2] Fujian Normal Univ, Ctr Appl Math Fujian Prov FJNU, Fujian Key Lab Math Anal & Applicat FJKLMAA, Coll Math & Informat, Fuzhou 350007, Peoples R China

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2021年 / 34卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Feller process; Hunt process; Lower bounded semi-Dirichlet form; Martingale; Jumping kernel; Law of the iterated logarithm; DIFFUSION;

D O I：

10.1007/s10959-020-01035-8

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 present sufficient conditions, in terms of the jumping kernels, for two large classes of conservative Markov processes of pure-jump type to be purely discontinuous martingales with finite second moment. As an application, we establish the law of the iterated logarithm for sample paths of the associated processes.

引用

页码：2005 / 2032

页数：28

共 50 条

[1] Martingale Nature and Laws of the Iterated Logarithm for Markov Processes of Pure-Jump Type
Yuichi Shiozawa
Jian Wang
Journal of Theoretical Probability, 2021, 34 : 2005 - 2032
[2] Laws of the iterated logarithm for symmetric jump processes
Kim, Panki
Kumagai, Takashi
Wang, Jian
BERNOULLI, 2017, 23 (4A) : 2330 - 2379
[3] Laws of the iterated logarithm for occupation times of Markov processes
Cho, Soobin
Kim, Panki
Lee, Jaehun
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2025, 181
[4] Scalar conservation laws with monotone pure-jump Markov initial conditions
David C. Kaspar
Fraydoun Rezakhanlou
Probability Theory and Related Fields, 2016, 165 : 867 - 899
[5] Scalar conservation laws with monotone pure-jump Markov initial conditions
Kaspar, David C.
Rezakhanlou, Fraydoun
PROBABILITY THEORY AND RELATED FIELDS, 2016, 165 (3-4) : 867 - 899
[6] Laws of the iterated logarithm for a class of iterated processes
Nane, Erkan
STATISTICS & PROBABILITY LETTERS, 2009, 79 (16) : 1744 - 1751
[7] Laws of the iterated logarithm for iterated Wiener processes
Hu, Y
PierreLotiViaud, D
Shi, Z
JOURNAL OF THEORETICAL PROBABILITY, 1995, 8 (02) : 303 - 319
[8] Martingale Approach to Optimal Portfolio-Consumption Problems in Markov-Modulated Pure-Jump Models
Lopez, Oscar
Serrano, Rafael
STOCHASTIC MODELS, 2015, 31 (02) : 261 - 291
[9] The law of iterated logarithm for additive functionals and martingale additive functionals of Harris recurrent Markov processes
Locherbach, Eva
Loukianova, Dasha
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2009, 119 (07) : 2312 - 2335
[10] LAWS OF THE ITERATED LOGARITHM FOR SYMMETRIC STABLE PROCESSES
GRIFFIN, PS
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1985, 68 (03): : 271 - 285

← 1 2 3 4 5 →