The Dynamic Spread of the Forward CDS with General Random Loss by Kun Tian, Dewen Xiong, Zhongxing Ye

“…We assume that the filtration F is generated by a d-dimensional Brownian motion W=(W1,…,Wd)′ as well as an integer-valued random measure μ(du,dy). …”
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Liquid Phase Separation Mechanism of Cu-40 wt.% Pb Hypermonotectic Alloys by Xiaosi Sun, Weixin Hao, Teng Ma, Junting Zhang, Guihong Geng

“…The liquid phase separation mechanism in the systems with stable miscibility gaps mainly involved Ostwald ripening, Brownian motion, Marangoni migration, and Stokes motion. …”
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Portfolio Selection with Liability and Affine Interest Rate in the HARA Utility Framework by Hao Chang, Kai Chang, Ji-mei Lu

“…This paper studied an asset and liability management problem with stochastic interest rate, where interest rate is assumed to be governed by an affine interest rate model, while liability process is driven by the drifted Brownian motion. The investors wish to look for an optimal investment strategy to maximize the expected utility of the terminal surplus under hyperbolic absolute risk aversion (HARA) utility function, which consists of power utility, exponential utility, and logarithm utility as special cases. …”
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Determination of Protein Amount in Nanosized Synthetic Liposomes by Surface Effect Raman Spectroscopy (SERS) by Şeyma Parlatan

“…The size distribution of the trapped liposomes (140 nm on average) was found by using Einstein's Brownian motion equation, consistent with the size distribution obtained from dynamic light scattering measure-ments. …”
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Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model by A. A. Elmandouh, M. E. Elbrolosy

“…The Ivancevic option pricing model comes as an alternative to the Black-Scholes model and depicts a controlled Brownian motion associated with the nonlinear Schrodinger equation. …”
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Proactive Hedging European Call Option Pricing with Linear Position Strategy by Meng Li, Xuefeng Wang, Fangfang Sun

“…In this study, the underlying asset price movement is assumed to follow geometric fractional Brownian motion. The pricing formula for proactive hedging call options is derived with a linear position strategy by applying the risk-neutral evaluation principle. …”
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Emergence of opposing arrows of time in open quantum systems by Thomas Guff, Chintalpati Umashankar Shastry, Andrea Rocco

“…This imposes a time-symmetric formulation of quantum Brownian motion, Lindblad and Pauli master equations, which hence describe thermalisation that may occur into two opposing time directions. …”
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Physical Mechanisms and Theoretical Computation of Efficiency of Submicron Particles Agglomeration by Nonlinear Acoustic Influence by Vladimir N. Khmelev, Andrey V. Shalunov, Roman N. Golykh

“…The nonlinear effects of the shock waves (the transfer of heat, drop in pressure, change in the particles’ collisional cross-section due to Brownian motion, and difference in particle concentration), which influence the particle coagulation rate, are simulated for the first time and evaluated. …”
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Spectral Collocation Method for Fractional Differential/Integral Equations with Generalized Fractional Operator by Qinwu Xu, Zhoushun Zheng

“…Further, based on the proposed method, a kind of generalized grey Brownian motion is simulated and properties of the model are analyzed.…”
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A continuous phenotype space model of RNA virus evolution within a host by Andrei Korobeinikov, Conor Dempsey

“…Due to their very high replication and mutation rates, RNA virusescan serve as an excellent testing model for verifying hypothesis andaddressing questions in evolutionary biology.In this paper, we suggest a simple deterministic mathematical modelof the within-host viral dynamics, where a possibility for random mutations incorporates.This model assumes a continuous distribution of viral strainsin a one-dimensional phenotype space where random mutations aremodelled by Brownian motion (that is, by diffusion).Numerical simulations show that randommutations combined with competition for a resource result in evolutiontowards higher Darwinian fitness: a stable pulse traveling waveof evolution, moving towards higher levels of fitness,is formed in the phenotype space.The advantage of this model, compared with the previously constructedmodels, is that this model is mechanistic and is based on commonlyaccepted model of virus dynamics within a host, and thus it allowsan incorporation of features of the real-life host-virus system such as immuneresponse, antiviral therapy, etc.…”
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IMPACT OF CHEMICAL REACTION ON MHD BOUNDARY LAYER FLOW OF NANOFLUIDS OVER A NONLINEAR STRETCHING SHEET WITH THERMAL RADIATION HAAR WAVELET COLLOCATION METHOD by MAHESH KUMAR N, Vishwanath B Awati, Akash Goravar

“…It predicts that, the local Sherwood number increases with increase in the parameters of Brownian motion and thermophoresis. For both temperature and volume fraction profiles decreases due to an increase in the Schmidt number.…”
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Evaluation Formulas for Generalized Conditional Wiener Integrals with Drift on a Function Space by Dong Hyun Cho

“…In this paper we derive a translation theorem for a generalized Wiener integral and then prove that Y is a generalized Brownian motion process with drift a. Furthermore, we derive two simple formulas for generalized conditional Wiener integrals of functions on C[0,t] with the drift and the conditioning functions Yn and Yn+1. …”
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Evolution of Bounded Confidence Opinion in Social Networks by Hui Xie, Guangjian Li, Yongjie Yan, Sihui Shu

“…However, since agents want to evolve their opinion with Brownian motion, which may in turn impede full consensus, sufficiently frequent long-range links are in such situations crucial for the network to converge into an absorbing phase. …”
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The Magnetohydrodynamic Boundary Layer Flow of a Nanofluid past a Stretching/Shrinking Sheet with Slip Boundary Conditions by Syahira Mansur, Anuar Ishak

“…The local Nusselt number is lower for higher values of Lewis number, Brownian motion parameter, and thermophoresis parameter.…”
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Application of BSDE in Standard Inventory Financing Loan by Hui Zhang, Wenyu Meng, Xiaojie Wang, Jianwei Zhang

“…We assume that the short-term prices of the collateral follow a geometric Brownian motion. We use a set of equivalent martingale measures to build the models about a bank’s maximum and minimum levels of risk tolerance in an environment with Knightian uncertainty. …”
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Fractional Order Stochastic Differential Equation with Application in European Option Pricing by Qing Li, Yanli Zhou, Xinquan Zhao, Xiangyu Ge

“…In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study.…”
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Modeling and Analysis of Dynamic Social Ties in D2D Collaborative Video Transmission by Qi Zhang, Zufan Zhang, Tian Zeng, Xiaoke Li

“…Specifically, a stochastic mathematical model is established and analyzed, in which the combined effect of many factors such as interest, geographical position, career, social class, value system, and interaction is considered. Based on the Brownian motion theory, the strength of social ties among social individuals with time is studied. …”
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Inclined Magnetic Field on Mixed Convection Darcy–Forchheimer Maxwell Nanofluid Flow Over a Permeable Stretching Sheet With Variable Thermal Conductivity: The Numerical Approach by Gossaye Aliy Adem, Adamu Gizachew Chanie

“…A number of parameters are looked at, such as the response rate constant, mixed convection, buoyancy ratio, suction/injection, Brownian motion, Lewis number, and thermophoresis. Interestingly, the results show that activation energy and mixed convection parameters, respectively, have an increasing effect on concentration and velocity curves.…”
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Hydromagnetic Stability of Metallic Nanofluids (Cu-Water and Ag-Water) Using Darcy-Brinkman Model by J. Ahuja, U. Gupta, R. K. Wanchoo

“…Thermal convection of a nanofluid layer in the presence of imposed vertical magnetic field saturated by a porous medium is investigated for both-free, rigid-free, and both-rigid boundaries using Darcy-Brinkman model. The effects of Brownian motion and thermophoretic forces due to the presence of nanoparticles and Lorentz’s force term due to the presence of magnetic field have been considered in the momentum equations along with Maxwell’s equations. …”
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Theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold by Iker Pascual de Zulueta, Angel Valle

“…We find the conditions for which the evolution in those rate equations can be described by 1-dimensional and two dimensional Brownian motions, respectively. The main statistical differences between the additive and multiplicative noise models are then illustrated by using the simplified Brownian motion models. …”
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