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A modified Φ-Sobolev inequality for canonical Lévy processes and its applications
Modern Stochastics: Theory and Applications, 2023 A new modified Φ-Sobolev inequality for canonical ${L^{2}}$-Lévy processes, which are hybrid cases of the Brownian motion and pure jump-Lévy processes, is developed.
Noriyoshi Sakuma, Ryoichi Suzuki
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Brownian motion and magnetism [PDF]
Physical Review B, 1994 Published
Sinha, Supurna, Samuel, Joseph
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Scaled Brownian motion with renewal resetting. [PDF]
Physical Review E, 2018 We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient D(t)∼t^{α-1} with α>0 (scaled Brownian motion) is stochastically reset to its initial position, and starts anew. In the present work
A. Bodrova, A. Chechkin, I. Sokolov
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Probability Theory and Related Fields, 2013 We consider processes which have the distribution of standard Brownian motion (in the forward direction of time) starting from random points on the trajectory which accumulate at $-\infty$. We show that these processes do not have to have the distribution of standard Brownian motion in the backward direction of time, no matter which random time we take
Krzysztof Burdzy, Michael Scheutzow
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Biosensors, 2022 Brownian motion, which is a natural phenomenon, has attracted numerous researchers and received extensive studies over the past decades. The effort contributes to the discovery of optical diffusometry, which is commonly used for micro/nano particle ...
Wei-Long Chen, Han-Sheng Chuang
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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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Properties of additive functionals of Brownian motion with resetting [PDF]
Journal of Physics A: Mathematical and Theoretical, 2018 We study the distribution of additive functionals of reset Brownian motion, a variation of normal Brownian motion in which the path is interrupted at a given rate and placed back to a given reset position.
F. den Hollander +3 more
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Limiting Behaviors for Brownian Motion Reflected on Brownian Motion [PDF]
Methods and Applications of Analysis, 2002 Suppose that g(t) and Wt are independent Brownian motions starting from g(0) = W0 = 0. Consider the Brownian motion Yt reflected on g(t), obtained from Wt by the means of the Skorohod lemma. The upper and lower limiting behaviors of Yt are presented. The upper tail estimate on exit time is computed via principal eigenvalue.
Chen, X., Li, Wenbo
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Active Brownian motion in two dimensions [PDF]
Physical Review E, 2018 We study the dynamics of a single active Brownian particle (ABP) in two spatial dimensions. The ABP has an intrinsic timescale ${D}_{R}^{\ensuremath{-}1}$ set by the rotational diffusion constant ${D}_{R}$. We show that, at short times $t\ensuremath{\ll}{
U. Basu +3 more
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