Results 11 to 20 of about 3,960 (256)

Fractional Brownian Motions [PDF]

Acta Physica Polonica B, 2020
Properties of different models of fractional Brownian motions are discussed in detail. We shall collect here several possible ways of introducing and defining various possible fBms, discuss their properties, find how they are similar, and how they differ.
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Averaging Principle for Caputo Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion with Delays

Complexity, 2021
In this article, we investigate a class of Caputo fractional stochastic differential equations driven by fractional Brownian motion with delays. Under some novel assumptions, the averaging principle of the system is obtained.
Pengju Duan, Hao Li, Jie Li, Pei Zhang
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The Influence of Multiplicative Noise and Fractional Derivative on the Solutions of the Stochastic Fractional Hirota–Maccari System

Axioms, 2022
We address here the space-fractional stochastic Hirota–Maccari system (SFSHMs) derived by the multiplicative Brownian motion in the Stratonovich sense. To acquire innovative elliptic, trigonometric and rational stochastic fractional solutions, we employ ...
Farah M. Al-Askar, Wael W. Mohammed, Clemente Cesarano, M. El-Morshedy   +3 more
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Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion

Complexity, 2021
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 ...
Weijun Ma, Wei Liu, Quanxin Zhu, Kaibo Shi   +3 more
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Asymptotics of the Persistence Exponent of Integrated Fractional Brownian Motion and Fractionally Integrated Brownian Motion [PDF]

Theory of Probability & Its Applications, 2022
Рассматривается вероятность персистентности для интегрированного дробного броуновского движения и дробно интегрированного броуновского движения с параметром $H$. Для интегрированного дробного броуновского движения обсуждается гипотеза Молчана- Хохлова и устанавливается асимптотическое поведение показателя персистентности при $H\to0$ и при $H\to1 ...
Aurzada, F., Kilian, M.
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Oscillatory Fractional Brownian Motion [PDF]

Acta Applicandae Mathematicae, 2013
The authors ``introduce oscillatory analogues of fractional Brownian motion [(fBm)], subfractional Brownian motion [(sfBm)] and other related long range dependent Gaussian processes.'' According to them, the oscillatory fractional Brownian motion (ofBm) is a centered Gaussian process \(\xi ^{H}\), with parameter \(H\in (1/2,1)\) and covariance function
Bojdecki, T., Gorostiza, L. G., Talarczyk, A.   +2 more
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Impact of Multiplicative Noise on the Exact Solutions of the Fractional-Stochastic Boussinesq-Burger System

Journal of Mathematics, 2022
In this paper, we consider the fractional-stochastic Boussinesq-Burger system (FSBBS) generated by the multiplicative Brownian motion. The Jacobi elliptic function techniques are used to create creative elliptic, hyperbolic, and rational fractional ...
Wael W. Mohammed, Farah M. Al-Askar, M. El-Morshedy   +2 more
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ON THE QHASI CLASS AND ITS EXTENSION TO SOME GAUSSIAN SHEETS

International Journal for Computational Civil and Structural Engineering, 2022
Introduced in 2018 the generalized bifractional Brownian motion is considered as an element of the quasi-helix with approximately stationary increment class of real centered Gaussian processes conditioning by parameters.
Charles El-Nouty, Darya Filatova
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Almost Periodic Solutions to Impulsive Stochastic Delay Differential Equations Driven by Fractional Brownian Motion With 12 < H < 1

Frontiers in Physics, 2021
In this article, we study the existence and uniqueness of square-mean piecewise almost periodic solutions to a class of impulsive stochastic functional differential equations driven by fractional Brownian motion.
Lili Gao, Xichao Sun
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Cluster Analysis on Locally Asymptotically Self-Similar Processes with Known Number of Clusters

Fractal and Fractional, 2022
We conduct cluster analysis of a class of locally asymptotically self-similar stochastic processes with finite covariance structures, which includes Brownian motion, fractional Brownian motion, and multifractional Brownian motion as paradigmatic examples.
Nan Rao, Qidi Peng, Ran Zhao
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