On the standard Brownian motion. I by Stasys Steišūnas

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Spectral Representation and Simulation of Fractional Brownian Motion by Konstantin Rybakov

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Universality in the dynamical phase transitions of Brownian motion by Takahiro Kanazawa, Kyogo Kawaguchi, Kyosuke Adachi

“…We next investigate how second-order DPTs can appear in one-dimensional free Brownian motion by choosing the observable, which essentially captures the localization transition of the trajectories. …”
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On the Fourier-Transformed Boltzmann Equation with Brownian Motion by Yong-Kum Cho, Eunsil Kim

“…We establish a global existence theorem, and uniqueness and stability of solutions of the Cauchy problem for the Fourier-transformed Fokker-Planck-Boltzmann equation with singular Maxwellian kernel, which may be viewed as a kinetic model for the stochastic time-evolution of characteristic functions governed by Brownian motion and collision dynamics.…”
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On the Self-Intersection Local Time of Subfractional Brownian Motion by Junfeng Liu, Zhihang Peng, Donglei Tang, Yuquan Cang

“…We study the problem of self-intersection local time of d-dimensional subfractional Brownian motion based on the property of chaotic representation and the white noise analysis.…”
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On weak convergence of an approximation of a fractional Brownian motion by Kęstutis Kubilius

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Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion by Yongchun Zhou, Xiaohui Ai, Minghao Lv, Boping Tian

“…Based on the norm in the Hilbert Space L2[0,1], the second order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the space spanned by nonlinear function subspace. …”
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The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment by Chao Wang, Shengwu Zhou, Jingyuan Yang

“…Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. …”
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Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus by Yuquan Cang, Junfeng Liu, Yan Zhang

“…Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motion SH1. We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion.…”
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Holographic Brownian Motion in Three-Dimensional Gödel Black Hole by J. Sadeghi, F. Pourasadollah, H. Vaez

“…In that case we follow Atmaja (2013) about Brownian motion in BTZ black hole. In this paper we receive some new results for the case of α2l2≠1. …”
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Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion by Long Shi, Aiguo Xiao

“…In a continuum limit, the process can be defined by an integrated Brownian motion subordinated by an inverse α-stable subordinator. …”
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SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions by Pengju Duan

“…The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. We prove the existence and uniqueness of the solutions to the backward stochastic differential equations by constructing Cauchy sequence and fixed point theorem. …”
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On approximation of stochastic integrals with respect to a fractional Brownian motion by Kęstutis Kubilius

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Stochastic Volterra Equation Driven by Wiener Process and Fractional Brownian Motion by Zhi Wang, Litan Yan

“…For a mixed stochastic Volterra equation driven by Wiener process and fractional Brownian motion with Hurst parameter H>1/2, we prove an existence and uniqueness result for this equation under suitable assumptions.…”
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An Averaging Principle for Stochastic Differential Delay Equations with Fractional Brownian Motion by Yong Xu, Bin Pei, Yongge Li

“…An averaging principle for a class of stochastic differential delay equations (SDDEs) driven by fractional Brownian motion (fBm) with Hurst parameter in (1/2,1) is considered, where stochastic integration is convolved as the path integrals. …”
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A note on local asymptotic behaviour for Brownian motion in Banach spaces by Mou-Hsiung Chang

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Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion by Weijun Ma, Wei Liu, Quanxin Zhu, Kaibo Shi

“…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. …”
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Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion by Yanmin Ouyang, Jingyuan Yang, Shengwu Zhou

“…The mixed fractional Brownian motion and the jump process were used to characterize the evolution of stock prices. …”
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The existence and uniqueness of the solution of the integral equation driven by fractional Brownian motion by Kęstutis Kubilius

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Fractional Brownian Motion for a System of Fuzzy Fractional Stochastic Differential Equation by Kinda Abuasbeh, Ramsha Shafqat

“…We study fractional Brownian motion– (FBM–) driven fuzzy stochastic fractional evolution equations. …”
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