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Brownian Motion of an Ellipsoid
Science, 2006We studied the Brownian motion of isolated ellipsoidal particles in water confined to two dimensions and elucidated the effects of coupling between rotational and translational motion. By using digital video microscopy, we quantified the crossover from short-time anisotropic to long-time isotropic diffusion and directly measured probability ...
Han, Yilong +5 more
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Catastrophes in Brownian motion
Physics Letters A, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guz SA, MANNELLA, RICCARDO, Sviridov MV
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2020
[en] The aim of this work is to study the Brownian motion from a theoretical approach. Brownian motion (also named Wiener process) is one of the best known stochastic processes and plays an important role in both pure and applied Mathematics. In the first chapter, we present the basic concepts of the theory of stochastic processes such as filtrations ...
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[en] The aim of this work is to study the Brownian motion from a theoretical approach. Brownian motion (also named Wiener process) is one of the best known stochastic processes and plays an important role in both pure and applied Mathematics. In the first chapter, we present the basic concepts of the theory of stochastic processes such as filtrations ...
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1969
Publisher Summary This chapter discusses the Brownian motion, and reviews the construction of the Brownian motion. The simplest properties of the Brownian motion are discussed. A Martingale inequality is discussed, and the law of the iterated logarithm is reviewed. Several-dimensional Brownian motion is also discussed in the chapter.
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Publisher Summary This chapter discusses the Brownian motion, and reviews the construction of the Brownian motion. The simplest properties of the Brownian motion are discussed. A Martingale inequality is discussed, and the law of the iterated logarithm is reviewed. Several-dimensional Brownian motion is also discussed in the chapter.
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Physical Review Letters, 1983
A new master equation describing the irreversible process of a quantum mechanical Brownian particle is proposed. The master equation is shown to obey the symmetry of detailed balance leading to a quantum analog of the reciprocity relations, and the fluctuation-dissipation theorem is obtained. The method is applied to the damped harmonic oscillator. The
Grabert, Hermann, Talkner, Peter
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A new master equation describing the irreversible process of a quantum mechanical Brownian particle is proposed. The master equation is shown to obey the symmetry of detailed balance leading to a quantum analog of the reciprocity relations, and the fluctuation-dissipation theorem is obtained. The method is applied to the damped harmonic oscillator. The
Grabert, Hermann, Talkner, Peter
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Brownian Motion on a Hypersurface
Bulletin of the London Mathematical Society, 1985Let \(f:R^ d\to R\) be a \(C^ 2\) function and let \(V=f^{-1}(c)\) be a level surface on which grad f(x) is never zero and orient V with the field n(\(\cdot)\) of normal vectors. Let H(x) be the mean curvature at x. We prove the following: 1. A process X in \(R^ d\) with \(f(X_ 0)=c\) and \(dX=dB n(X)+2^{-1}(d- 1)H(X)n(X)dt\) is a Brownian motion on ...
John T. Lewis, M. van den Berg
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On Equations of Brownian Motion
Theory of Probability & Its Applications, 1964A study is made of the relationships between the different descriptions of Brownian motion expressed as an integro-differential equation of Boltzmann type, as a Langevin equation and a partial differential equation corresponding to it, and as Fokker-Plank-Kolmogorov equations.
R. Z. Khas’minskii, A. M. Il’in
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Probability Theory and Related Fields, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wendelin Werner, Mihael Perman
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wendelin Werner, Mihael Perman
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Brownian Motion and Diffusions
2011Multi-skewed Brownian motion Bα = {Bαt: t ≥ 0} with skewness sequence α = {αk: k ∈ Z} and interface set S = {xk: k ∈ Z} is the solution to Xt = X0 + Bt + ∫R LX(t, x)dμ(x) with μ = ∑k∈Z(2αk - 1)δxk We assume that αk ∈ (0, 1)\{1/2} and that S has no accumulation points.
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