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Weak Convergence to Brownian Meander and Brownian Excursion
Annals of Probability, 1977 We show that (i) Brownian motion conditioned to be positive is Brownian meander; (ii) tied-down Brownian meander is Brownian excursion; and (iii) Brownian bridge conditioned to be positive is Brownian excursion. Using these results we derive the distribution of the suprema of the meander and excursion.
Durrett, Richard T. +2 more
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A Relation between Brownian Bridge and Brownian Excursion
Annals of Probability, 1979 It is shown that Brownian excursion is equal in distribution to Brownian bridge with the origin placed at its absolute minimum. This explains why the maximum of Brownian excursion and the range of Brownian bridge have the same distribution, a fact which was discovered by Chung and Kennedy.
exaly +4 more sources
Quantification of cell migration: metrics selection to model application
Frontiers in Cell and Developmental Biology, 2023 Cell migration plays an essential role in physiological and pathological states, such as immune response, tissue generation and tumor development.
Yang Hu +3 more
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Numerical Solution of Vasicek Equation by Using Brownian Wavelets and Multiple Ito-Integral [PDF]
Control and Optimization in Applied Mathematics, 2020 In this paper, we present a new approach to solving stochastic differential equations and the Vasicek equation by using Brownian wavelets and multiple Ito-integral.
Mahmoud Mahmoudi +1 more
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Demonstratio Mathematica, 2021 A revised model of the nanoparticle mass flux is introduced and used to study the thermal instability of the Rayleigh-Benard problem for a horizontal layer of nanofluid heated from below.
Alharbi Ozwah S., Abdullah Abdullah A.
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Physical Review Letters, 2006 Onsager symmetry implies that a Brownian motor, driven by a temperature gradient, will also perform a refrigerator function upon loading. We analytically calculate the corresponding heat flux for an exactly solvable microscopic model and compare it with molecular dynamics simulations.
Van den Broeck, C., Kawai, R.
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Proceedings of the National Academy of Sciences, 2002 Arratia, [Arratia, R. (1979) Ph.D. thesis (University of Wisconsin, Madison) and unpublished work] and later Toth and Werner [Toth, B. & Werner, W. (1998) Probab. Theory Relat. Fields 111, 375–452] constructed random processes that formally correspond to coalescing one-dimensional Brownian motions starting from ...
FONTES L.R. +3 more
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The flashing Brownian ratchet and Parrondo’s paradox [PDF]
Royal Society Open Science, 2018 A Brownian ratchet is a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. A flashing Brownian ratchet is a process that alternates between two regimes, a one-dimensional Brownian motion and a ...
S. N. Ethier, Jiyeon Lee
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ON THE QHASI CLASS AND ITS EXTENSION TO SOME GAUSSIAN SHEETS
International Journal for Computational Civil and Structural Engineering, 2022 Introduced in 2018 the generalized bifractional Brownian motion is considered as an element of the quasi-helix with approximately stationary increment class of real centered Gaussian processes conditioning by parameters.
Charles El-Nouty, Darya Filatova
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Compact Brownian surfaces I: Brownian disks [PDF]
Probability Theory and Related Fields, 2017 We show that, under certain natural assumptions, large random plane bipartite maps with a boundary converge after rescaling to a one-parameter family ($\mathrm{BD}_L$, $0 < L < \infty$) of random metric spaces homeomorphic to the closed unit disk of $\mathbb{R}^2$, the space $\mathrm{BD}_L$ being called the Brownian disk of perimeter $L$ and unit
Bettinelli, Jérémie, Miermont, Gregory
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