Results 21 to 30 of about 1,696,206 (346)
Square of Brownian motion [PDF]
Nagoya Mathematical Journal, 1975 Let Xt be a stochastic process and Yt be its square process. The present note is concerned with the solution of the equation assuming Yt is given. In [4], F. A. Grünbaum proved that certain statistics of Yt are enough to determine those of Xt when it is a centered, nonvanishing, Gaussian process with continuous correlation function. In connection with
Hisao Nomoto
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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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The spans in Brownian motion [PDF]
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2017 33 pages, 4 figures.
Evans, Steven, Pitman, Jim, Tang, Wenpin
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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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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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Physical Review Letters, 2010 We derive the generalized Markovian description for the non-equilibrium Brownian motion of a heated particle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and Stokes-Einstein relations compare favorably with measurements of laser-heated gold nano-particles and provide a ...
Romy Schachoff +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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An optimal polynomial approximation of Brownian motion [PDF]
, 2020 In this paper, we will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. The coefficients that are obtained from the expansion of Brownian motion in this polynomial basis are independent ...
Foster, James +2 more
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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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