Corrigendum: Large deviations for multi-dimensional reflected fractional Brownian motion

2004 ◽  
Vol 76 (5) ◽  
pp. 479-479 ◽  
Author(s):  
Kurt Majewski
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Fractional Brownian Motion

Large deviations and Berry–Esseen inequalities for estimators in nonhomogeneous diffusion driven by fractional Brownian motion

2020 ◽  
Vol 28 (3) ◽  
pp. 183-196
Author(s):  
Kouacou Tanoh ◽  
Modeste N’zi ◽  
Armel Fabrice Yodé
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Maximum Likelihood ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Maximum Likelihood Estimator ◽  
Bayes Estimator ◽  
Likelihood Estimator

AbstractWe are interested in bounds on the large deviations probability and Berry–Esseen type inequalities for maximum likelihood estimator and Bayes estimator of the parameter appearing linearly in the drift of nonhomogeneous stochastic differential equation driven by fractional Brownian motion.

scholarly journals Large deviations of Shepp statistics for fractional Brownian motion

2013 ◽  
Vol 83 (10) ◽  
pp. 2242-2247 ◽  
Author(s):  
Enkelejd Hashorva ◽  
Zhongquan Tan
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Fractional Brownian Motion

scholarly journals Large deviations for optimal filtering with fractional Brownian motion

2013 ◽  
Vol 123 (6) ◽  
pp. 2340-2352 ◽  
Author(s):  
Vasileios Maroulas ◽  
Jie Xiong
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Fractional Brownian Motion ◽  
Optimal Filtering

Large deviations for multi-dimensional reflected fractional Brownian motion

2003 ◽  
Vol 75 (4) ◽  
pp. 233-257 ◽  
Author(s):  
Kurt Majewski
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Fractional Brownian Motion

scholarly journals Large deviations for subordinated fractional Brownian motion and applications

2018 ◽  
Vol 458 (2) ◽  
pp. 1678-1692 ◽  
Author(s):  
Weigang Wang ◽  
Zhenlong Chen
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Fractional Brownian Motion

scholarly journals Large deviations for local time fractional Brownian motion and applications

2008 ◽  
Vol 346 (2) ◽  
pp. 432-445 ◽  
Author(s):  
Mark M. Meerschaert ◽  
Erkan Nane ◽  
Yimin Xiao
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Fractional Brownian Motion ◽  
Local Time

scholarly journals Asymptotics of Karhunen–Loève Eigenvalues for Sub-Fractional Brownian Motion and Its Application

2021 ◽  
Vol 5 (4) ◽  
pp. 226
Author(s):  
Chun-Hao Cai ◽  
Jun-Qi Hu ◽  
Ying-Li Wang
Keyword(s):  
Functional Analysis ◽  
Brownian Motion ◽  
Asymptotic Analysis ◽  
Large Deviations ◽  
Fractional Brownian Motion ◽  
Analysis Method ◽  
Large N

In the present paper, the Karhunen–Loève eigenvalues for a sub-fractional Brownian motion are considered. Rigorous large n asymptotics for those eigenvalues are shown, based on the functional analysis method. By virtue of these asymptotics, along with some standard large deviations results, asymptotical estimates for the small L2-ball probabilities for a sub-fractional Brownian motion are derived. Asymptotic analysis on the Karhunen–Loève eigenvalues for the corresponding “derivative” process is also established.

LARGE DEVIATIONS FOR PERTURBED REFLECTED DIFFUSION PROCESSES DRIVEN BY A FRACTIONAL BROWNIAN MOTION IN HOLDERIAN NORM

2020 ◽  
Vol 9 (3) ◽  
pp. 839-858
Author(s):  
R.A. Randrianomenjanahary ◽  
D. M. Rakotoniriana ◽  
T. J. Rabeherimanana
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Fractional Brownian Motion ◽  
Diffusion Processes ◽  
Reflected Diffusion

scholarly journals Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Weijun Ma ◽  
Wei Liu ◽  
Quanxin Zhu ◽  
Kaibo Shi
Keyword(s):  
Brownian Motion ◽  
Population Growth ◽  
Large Deviations ◽  
Exponential Stability ◽  
Fractional Brownian Motion ◽  
Large Deviation ◽  
Mixed Fractional Brownian Motion ◽  
Growth System ◽  
Exponential Population Growth ◽  
Exponential Population

This paper examines the dynamics of the exponential population growth system with mixed fractional Brownian motion. First, we establish some useful lemmas that provide powerful tools for studying the stochastic differential equations with mixed fractional Brownian motion. We offer some explicit expressions and numerical characteristics such as mathematical expectation and variance of the solutions of the exponential population growth system with mixed fractional Brownian motion. Second, we propose two sufficient and necessary conditions for the almost sure exponential stability and the k th moment exponential stability of the solution of the constant coefficient exponential population growth system with mixed fractional Brownian motion. Furthermore, we conduct some large deviation analysis of this mixed fractional population growth system. To the best of the authors’ knowledge, this is the first paper to investigate how the Hurst index affects the exponential stability and large deviations in the biological population system. It is interesting that the phenomenon of large deviations always occurs for addressed system when 1 / 2 < H < 1 . Moreover, several numerical simulations are reported to show the effectiveness of the proposed approach.

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