Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion by Di Pan, Shengwu Zhou, Yan Zhang, Miao Han

“…The numerical experiments show that Hurst exponent of the fractional Brownian motion and transaction cost rate have a significant impact on the option value.…”
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Parameter Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion by Na Song, Zaiming Liu

“…We study the asymptotic properties of minimum distance estimator of drift parameter for a class of nonlinear scalar stochastic differential equations driven by mixed fractional Brownian motion. The consistency and limit distribution of this estimator are established as the diffusion coefficient tends to zero under some regularity conditions.…”
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Transportation Inequalities for Coupled Fractional Stochastic Evolution Equations Driven by Fractional Brownian Motion by Wentao Zhan, Yuanyuan Jing, Liping Xu, Zhi Li

“…In this paper, we consider the existence and uniqueness of the mild solution for a class of coupled fractional stochastic evolution equations driven by the fractional Brownian motion with the Hurst parameter H∈1/4,1/2. Our approach is based on Perov’s fixed-point theorem. …”
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Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion by Henryk Leszczyński, Monika Wrzosek

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Asian Option Pricing with Transaction Costs and Dividends under the Fractional Brownian Motion Model by Yan Zhang, Di Pan, Sheng-Wu Zhou, Miao Han

“…The pricing problem of geometric average Asian option under fractional Brownian motion is studied in this paper. The partial differential equation satisfied by the option’s value is presented on the basis of no-arbitrage principle and fractional formula. …”
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The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion by Zulqurnain Sabir, Assad Ayub, Juan L. G. Guirao, Saira Bhatti, Syed Zahir Hussain Shah

“…The present study is related to the effects of activation energy and thermophoretic diffusion on steady micropolar fluid along with Brownian motion. The activation energy and thermal conductivity of steady micropolar fluid are also discussed. …”
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Exploring the impact of Brownian motion on novel closed-form solutions of the extended Kairat-II equation by Khaled Aldwoah, Alaa Mustafa, Tariq Aljaaidi, Khidir Mohamed, Amer Alsulami, Mohammed Hassan

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Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion by Yuling Wang, Jing Wang

“…This paper studies the pricing of American carbon emission derivatives and its numerical method under the mixed fractional Brownian motion. To capture the long memory properties such as self-similarity and long-range dependence in the price process, we proposed a model based on a fractional Black–Scholes, which is more in line with the actual characteristics of the option market. …”
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Averaging Principle for Caputo Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion with Delays by Pengju Duan, Hao Li, Jie Li, Pei Zhang

“…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. …”
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The Fundamental Aspects of TEMOM Model for Particle Coagulation due to Brownian Motion—Part II: In the Continuum Regime by He Qing, Xie Mingliang

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Quantum Brownian motion induced by a scalar field in Einstein’s universe under Dirichlet and Neumann boundary conditions by E. J. B. Ferreira, H. F. Santana Mota

“…Abstract In this paper, the quantum Brownian motion of a point particle induced by the quantum vacuum fluctuations of a real massless scalar field in Einstein’s universe under Dirichlet and Neumann boundary conditions is studied. …”
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Pricing of Two Kinds of Power Options under Fractional Brownian Motion, Stochastic Rate, and Jump-Diffusion Models by Kaili Xiang, Yindong Zhang, Xiaotong Mao

“…Option pricing is always one of the critical issues in financial mathematics and economics. Brownian motion is the basic hypothesis of option pricing model, which questions the fractional property of stock price. …”
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Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion by Jia Mu, Jiecuo Nan, Yong Zhou

“…In addition, with the fixed-point theorem and the properties of Mittag–Leffler functions, some results of the existence as well as asymptotic stability of square-mean S-asymptotically periodic solutions to a fractional stochastic diffusion equation with fractional Brownian motion are obtained. In the end, an example of numerical simulation is given to illustrate the effectiveness of our theory results.…”
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Geometric Brownian Motion-Based Time Series Modeling Methodology for Statistical Autocorrelated Process Control: Logarithmic Return Model by Siaw Li Lee, Chin Ying Liew, Chee Khium Chen, Li Li Voon

“…In addressing this gap, a novel time series modeling technique with its conceptual assumptions of attributes that was derived from the geometric Brownian motion (GBM) law was developed in this study. …”
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Fractional-Stochastic Solutions for the Generalized (2+1)-Dimensional Nonlinear Conformable Fractional Schrödinger System Forced by Multiplicative Brownian Motion by Sahar Albosaily, Wael W. Mohammed, Ekram E. Ali, R. Sidaoui, E. S. Aly, M. El-Morshedy

“…Finally, we illustrate that the multiplicative Brownian motion stabilizes the solutions of NCFSSS a round zero.…”
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On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function by Tristan Guillaume

“…This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. …”
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Harmonic Bernoulli strings and random permutations by Eugenius Manstavičius

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Entropy optimized nanomaterial flow with Soret and Dufour impacts by Tasawar Hayat, Aimen Tahir, Aneeta Razaq, Sohail A. Khan

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Endothermic and exothermic reactions and stagnation point nanofluid flow over a porous stretched surface with a revised Buongiorno model by R.P. Ashrith, K.V. Nagaraja, P. Nimmy, Pinank Patel, Ankur Kulshreshta, J.K. Madhukesh, Chander Prakash

Subjects: “…Thermophoresis and Brownian motion…”
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Heat transportation of 3D chemically reactive flow of Jeffrey nanofluid over a porous frame with variable thermal conductivity by Nahid Fatima, Aaqib Majeed, Taoufik Saidani, Nouman Ijaz, Kamal Barghout, Nidal Abu-Libdeh

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