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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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Limits of bifractional Brownian noises [PDF]
, 2008 Let $B^{H,K}=(B^{H,K}_{t}, t\geq 0)$ be a bifractional Brownian motion with two parameters $H\in (0,1)$ and $K\in(0,1]$. The main result of this paper is that the increment process generated by the bifractional Brownian motion $(B^{H,K}_{h+t} -B^{H,K}_{h}
Maejima, Makoto, Tudor, Ciprian
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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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100 years of Einstein's theory of Brownian motion: from pollen grains to protein trains [PDF]
, 2005 Experimental verification of the theoretical predictions made by Albert Einstein in his paper, published in 1905, on the molecular mechanisms of Brownian motion established the existence of atoms.
Chowdhury, Debashish
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Is a Brownian Motion Skew? [PDF]
Scandinavian Journal of Statistics, 2013 ABSTRACTWe study the asymptotic behaviour of the maximum likelihood estimator corresponding to the observation of a trajectory of a skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the limiting distribution when the step size goes to zero, which in this case are non‐classical, under the null ...
Ernesto Mordecki +4 more
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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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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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Rearrangements of Brownian motion [PDF]
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1974 Robert Kaufman
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