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
收藏
页码：1802 / 1812
页数：11
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