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Handbook of Brownian Motion - Facts and Formulae
, 1996 I: Theory.- I. Stochastic processes in general.- II. Linear diffusions.- III. Stochastic calculus.- IV. Brownian motion.- V. Local time as a Markov process.- VI. Differential systems associated to Brownian motion.- Appendix 1. Briefly on some diffusions.-
A. Borodin, P. Salminen
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Stochastic resetting in underdamped Brownian motion [PDF]
Journal of Statistical Mechanics: Theory and Experiment, 2018 We consider a single Brownian particle in one dimension in a medium at a constant temperature in the underdamped regime. We stochastically reset the position of the Brownian particle to a fixed point in the space with a constant rate r whereas its ...
D. Gupta
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Exact distributions of the maximum and range of random diffusivity processes
New Journal of Physics, 2021 We study the extremal properties of a stochastic process x _t defined by the Langevin equation ${\dot {x}}_{t}=\sqrt{2{D}_{t}}\enspace {\xi }_{t}$ , in which ξ _t is a Gaussian white noise with zero mean and D _t is a stochastic ‘diffusivity’, defined as
Denis S Grebenkov +4 more
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Pricing European Options under a Fuzzy Mixed Weighted Fractional Brownian Motion Model with Jumps
Fractal and Fractional, 2023 This study investigates the pricing formula for European options when the underlying asset follows a fuzzy mixed weighted fractional Brownian motion within a jump environment.
Feng Xu, Xiao-Jun Yang
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Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion [PDF]
Scientific Reports, 2016 It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit.
A. Bodrova +5 more
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Deterministic Brownian motion [PDF]
Physical Review A, 1992 The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscpoic derivation of the Fokker-Planck equation.
Paolo Grigolini +2 more
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Inertial effects of self-propelled particles: From active Brownian to active Langevin motion. [PDF]
Journal of Chemical Physics, 2019 Active particles that are self-propelled by converting energy into mechanical motion represent an expanding research realm in physics and chemistry. For micrometer-sized particles moving in a liquid ("microswimmers"), most of the basic features have been
H. Löwen
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On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes
Mathematics, 2019 We investigate the main statistical parameters of the integral over time of the fractional Brownian motion and of a kind of pseudo-fractional Gaussian process, obtained as a classical Gauss−Markov process from Doob representation by replacing ...
Mario Abundo, Enrica Pirozzi
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Microhydrodynamics, Brownian Motion, and Complex Fluids
, 2018 This text is an introduction to the dynamics of fluids at small scales, the physical and mathematical underpinnings of Brownian motion, and the application of these subjects to the dynamics and flow of complex fluids such as colloidal suspensions and ...
M. Graham
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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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