Results 21 to 30 of about 17,710,470 (300)
Square-root boundaries for Bessel processes and the hitting times of radial Ornstein-Uhlenbeck processes [PDF]
Opuscula Mathematica, 2023 This article deals with the first hitting times of a Bessel process to a square-root boundary. We obtain the explicit form of the distribution function of the hitting time by means of zeros of the confluent hypergeometric function with respect to the ...
Yuji Hamana
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Density of Generalized Verhulst Process and Bessel Process with Constant Drift
, 2016 Zhenyu Cui
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Asymptotic expansions for the first hitting times of Bessel processes [PDF]
Opuscula Mathematica, 2021 We study a precise asymptotic behavior of the tail probability of the first hitting time of the Bessel process. We deduce the order of the third term and decide the explicit form of its coefficient.
Yuji Hamana +2 more
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Parameter Estimation in Rough Bessel Model
Fractal and Fractional, 2023 In this paper, we construct consistent statistical estimators of the Hurst index, volatility coefficient, and drift parameter for Bessel processes driven by fractional Brownian motion with ...
Yuliya Mishura +1 more
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Nanophotonics, 2023 Nondiffracting Bessel surface plasmon polariton (SPP) beams, which have unique self-healing, non-divergence, and linear transmission properties, have charming applications in plasmonic devices and on-chip interconnection circuits.
Hu Hanmin +7 more
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Laser Scribing of Graphene Oxide Using Bessel Beam for Humidity Sensing
Advanced Devices & Instrumentation, 2023 Laser-scribed graphene oxide (GO) shows great promise for high-performance, cost-effective humidity sensors. However, when using the commonly employed Gaussian beam, the Rayleigh length is relatively short, leading to potential stability issues during ...
Ruo-Zhou Li, Jing Yan, Ke Qu, Ying Yu
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Micromachines, 2022 Speckle patterns are formed by random interferences of mutually coherent beams. While speckles are often considered as unwanted noise in many areas, they also formed the foundation for the development of numerous speckle-based imaging, holography, and ...
Vijayakumar Anand
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Some Processes Associated with Fractional Bessel Processes [PDF]
Journal of Theoretical Probability, 2005 Let $B=\{(B_{t}^{1},..., B_{t}^{d}), t\geq 0\}$ be a $d$-dimensional fractional Brownian motion with Hurst parameter $H$ and let $R_{t}=% \sqrt{(B_{t}^{1})^{2}+... +(B_{t}^{d})^{2}}$ be the fractional Bessel process. It 's formula for the fractional Brownian motion leads to the equation $ R_{t}=\sum_{i=1}^{d}\int_{0}^{t}\frac{B_{s}^{i}}{R_{s}}% dB_{s}^
Hu, Y., Nualart, D.
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A limit theorem for singular stochastic differential equations
Modern Stochastics: Theory and Applications, 2016 We study the weak limits of solutions to SDEs \[ dX_{n}(t)=a_{n}\big(X_{n}(t)\big)\hspace{0.1667em}dt+dW(t),\] where the sequence $\{a_{n}\}$ converges in some sense to $(c_{-}\mathbb{1}_{x0})/x+\gamma \delta _{0}$.
Andrey Pilipenko, Yuriy Prykhodko
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Super-efficient drilling of metals with ultrafast non diffractive laser beams
Scientific Reports, 2022 A highly efficient drilling process is found in non-transparent metallic materials enabled by the use of non-diffractive ultrafast Bessel beams. Applied for deep drilling through a 200 μm-thick steel plate, the Bessel beam demonstrates twofold higher ...
Huu Dat Nguyen +7 more
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