Square variation of Brownian paths in Banach spaces by Mou-Hsiung Chang

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Approximation of the first passage time density of a Wiener process to an exponentially decaying boundary by two-piecewise linear threshold. Application to neuronal spiking activit... by Massimiliano Tamborrino

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Option Pricing under the Subordinated Market Models by Longjin Lv, Changjuan Zheng, Luna Wang

“…This paper aims to study option pricing problem under the subordinated Brownian motion. Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity, leptokurtic, and long memory, which indicate that the fractional calculus can describe the financial data well. …”
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CFD Study on Wall/Nanoparticle Interaction in Nanofluids Convective Heat Transfer by Mohammad Reza Tarybakhsh, Ali Akbar Lotfi Neyestanak, Hamed Tarybakhsh

“…The Brownian motion of the nanoparticles in nanofluid is one of the potential contributors to enhance effective thermal conductivity and the mechanisms that might contribute to this enhancement are the subject of considerable discussion and debate. …”
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Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications by Longjin Lv, Luna Wang

“…Then, applying the subordinated Brownian motion into the option pricing problem, we obtain the closed-form pricing formula for the European option, when the underlying of the option contract is supposed to be driven by the subordinated geometric Brownian motion. …”
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Radiative Mixed Convection Flow of Casson Nanofluid through Exponentially Permeable Stretching Sheet with Internal Heat Generation by Mazhar Hussain, Shereen Fatima, Mubashir Qayyum

“…Temperature and concentration profiles show similar trends for Brownian motion, radiation, and thermophoresis.…”
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Analysis of water based Casson hybrid nanofluid (NiZnFe2O4+MnZnFe2O4) flow over an electromagnetic actuator with Cattaneo–Christov heat-mass flux: A modified Buongiorno model by S. Baskaran, R. Sowrirajan, S. Divya, S. Eswaramoorthi, K. Loganathan

“…The heat transfer rate enriches when elevating the quantities of radiation parameter and Biot number. Brownian motion and thermophoresis parameters reduce the mass transfer rate.…”
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Optimal Trade Execution under Jump Diffusion Process: A Mean-VaR Approach by Tianmin Zhou, Can Jia, Handong Li

“…In the classical optimal execution problem, the basic assumption of underlying asset price is Arithmetic Brownian Motion (ABM) or Geometric Brownian Motion (GBM). …”
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Numerical Solutions for Laminar Boundary Layer Nanofluid Flow along with a Moving Cylinder with Heat Generation, Thermal Radiation, and Slip Parameter by Titilayo Morenike Agbaje, Gilbert Makanda

“…The concentration profiles decrease with increasing radial coordinate. Increasing the Brownian motion and the thermophoresis parameter both destabilizes the concentration profiles. …”
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Pricing of Proactive Hedging European Option with Dynamic Discrete Position Strategy by Meng Li, Xuefeng Wang, Fangfang Sun

“…The observed price advantage is stronger when the underlying asset has more volatility or when the asset price follows closer to Geometric Brownian Motion. Additionally, we found that a higher frequency trading strategy has stronger price advantage if there is no trading cost. …”
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Numerical Solutions of Micropolar Nanofluid over an Inclined Surface Using Keller Box Analysis by Khuram Rafique, Hammad Alotaibi, Taher A. Nofal, Muhammad Imran Anwar, Masnita Misiran, Ilyas Khan

“…The Brownian motion and thermophoretic impacts attained a noticeable intention of the recent researchers because these factors trigger the thermal conductivity of the nanofluid. …”
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Local time statistics and permeable barrier crossing: From Poisson to birth-death diffusion equations by Toby Kay, Luca Giuggioli

“…We bridge this gap by developing a microscopic representation of Brownian motion in the presence of permeable barriers that allows us to treat barriers with constant asymmetric permeabilities. …”
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A Swarm Robotic Exploration Strategy Based on an Improved Random Walk Method by Bao Pang, Yong Song, Chengjin Zhang, Hongling Wang, Runtao Yang

“…The random walk methods that are used most commonly are Brownian motion and Lévy flight, both of which mimic the self-organized behavior of social insects. …”
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Mixed Convective-Radiative Dissipative Magnetized Micropolar Nanofluid Flow over a Stretching Surface in Porous Media with Double Stratification and Chemical Reaction Effects: ADM-... by P. K. Pattnaik, M. M. Bhatti, S. R. Mishra, Munawwar Ali Abbas, O. Anwar Bég

“…Temperatures are significantly enhanced with radiative parameter. Increasing Brownian motion parameter depletes concentration values. …”
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Stock volatility as an anomalous diffusion process by Rubén V. Arévalo, J. Alberto Conejero, Òscar Garibo-i-Orts, Alfred Peris

“…Our model computes the diffusion exponent of a financial time series to measure its volatility and it categorizes market movements into five diffusion models: annealed transit time motion (ATTM), continuous time random walk (CTRW), fractional Brownian motion (FBM), Lévy walk (LW), and scaled Brownian motion (SBM).Our findings suggest that the diffusion exponent derived from anomalous diffusion processes provides insightful and novel perspectives on stock market volatility. …”
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Relationships of convolution products, generalized transforms, and the first variation on function space by Seung Jun Chang, Jae Gil Choi

“…We use a generalized Brownian motion process to define the generalized Fourier-Feynman transform, the convolution product, and the first variation. …”
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An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model by A. S. Deakin, Matt Davison

“…The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms.…”
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Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme by Faiz Faizullah

“…We present the Cauchy-Maruyama (CM) approximation scheme and establish the existence theory of stochastic functional differential equations driven by G-Brownian motion (G-SFDEs). Several useful properties of Cauchy-Maruyama (CM) approximate solutions Xk of G-SFDEs are given. …”
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Topology of Locally and Non-Locally Generalized Derivatives by Dimiter Prodanov

“…There is a need for such generalizations when dealing with physical phenomena, such as fractures, shock waves, turbulence, Brownian motion, etc.…”
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Pricing Vulnerable Options in the Bifractional Brownian Environment with Jumps by Panhong Cheng, Zhihong Xu

“…In this paper, we study the valuation of European vulnerable options where the underlying asset price and the firm value of the counterparty both follow the bifractional Brownian motion with jumps, respectively. We assume that default event occurs when the firm value of the counterparty is less than the default boundary. …”
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