The non-Markovian property of q-Gaussian process

被引：0

作者：

Liu, Li-Min ^{[1
]}

Cui, Ying-Ying ^{[1
]}

Xu, Jie ^{[1
]}

Li, Chao ^{[1
]}

Gao, Qing-Hui ^{[1
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2020年 / 79卷 / 06期

关键词：

Tsallis entropy; q-Gaussian process; Non-Markovian; Self-similarity; Martingale; DYNAMICS;

D O I：

10.1016/j.camwa.2019.10.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the q-Gaussian process based on the non-extensive theory is discussed from a mathematical point of view, which has been widely applied to many anomalous diffusion systems in physics and finance. Firstly, the discussion of non-Markovian property of q-Gaussian process provides a numerical support for the future theoretical research. Secondly, the martingale and self-similarity of this process are obtained by Tsallis distributions. Thirdly, the long dependence is analyzed by simulations and Hurst exponents are compared with those of fractional Brownian motion. At last, the European call option price formula driven by this process is simulated, by which we find that this process can better match anomalous diffusion and the volatility smile. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：1802 / 1812

页数：11

共 50 条

[1] On optimal steering of a non-Markovian Gaussian process
Alpago, Daniele
Chen, Yongxin
Georgiou, Tryphon
Pavon, Michele
[J]. 2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC), 2019, : 2556 - 2561
[2] NON-MARKOVIAN PROCESSES WITH THE SEMIGROUP PROPERTY
FELLER, W
[J]. ANNALS OF MATHEMATICAL STATISTICS, 1959, 30 (04): : 1252 - 1253
[3] METHODS FOR NON-MARKOVIAN PROCESS
HARA, H
[J]. PROGRESS OF THEORETICAL PHYSICS, 1978, 60 (01): : 296 - 299
[4] Crossing intervals of non-Markovian Gaussian processes
Sire, Clement
[J]. PHYSICAL REVIEW E, 2008, 78 (01):
[5] Preservation of Quantum Coherence for Gaussian-State Dynamics in a Non-Markovian Process
文军
李冠强
[J]. Chinese Physics Letters, 2018, (06) : 6 - 10
[6] Preservation of Quantum Coherence for Gaussian-State Dynamics in a Non-Markovian Process
文军
李冠强
[J]. Chinese Physics Letters., 2018, 35 (06) - 10
[7] Preservation of Quantum Coherence for Gaussian-State Dynamics in a Non-Markovian Process
Wen, Jun
Li, Guan-Qiang
[J]. CHINESE PHYSICS LETTERS, 2018, 35 (06)
[8] NON-MARKOVIAN CUMULATIVE PROPERTY INSURANCE MODEL
Gorbenko, K. A.
[J]. VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-UPRAVLENIE VYCHISLITELNAJA TEHNIKA I INFORMATIKA-TOMSK STATE UNIVERSITY JOURNAL OF CONTROL AND COMPUTER SCIENCE, 2008, 2 (01): : 40 - 49
[9] Non-Markovian Quantum Process Tomography
White, G. A. L.
Pollock, F. A.
Hollenberg, L. C. L.
Modi, K.
Hill, C. D.
[J]. PRX QUANTUM, 2022, 3 (02):
[10] Non-Markovian Speedup Dynamics in Markovian and Non-Markovian Channels
Jing Nie
Yingshuang Liang
Biao Wang
Xiuyi Yang
[J]. International Journal of Theoretical Physics, 2021, 60 : 2889 - 2900

← 1 2 3 4 5 →