Nano-jet related to Bessel beams and to super-resolutions in microsphere optical experiments
EPJ Techniques and Instrumentation, 2017 The appearance of a Nano-jet in the microsphere optical experiments is analyzed by relating this effect to non-diffracting Bessel beams. By inserting a circular aperture with a radius of subwavelength dimension in the EM waist, and sending the ...
Yacob Ben-Aryeh
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Some explicit formulas for the Brownian bridge, Brownian meander and Bessel process under uniform sampling [PDF]
, 2013 We show that simple explicit formulas can be obtained for several relevant quantities related to the laws of the uniformly sampled Brownian bridge, Brownian meander and three dimensional Bessel process. To prove such results, we use the distribution of a
M. Rosenbaum, M. Yor
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The hard edge tacnode process and the hard edge Pearcey process with non-intersecting squared Bessel paths [PDF]
, 2014 A system of non-intersecting squared Bessel processes is considered which all start from one point and they all return to another point. Under the scaling of the starting and ending points when the macroscopic boundary of the paths touches the hard edge,
S. Delvaux, B'alint VetHo
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On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes [PDF]
, 2010 Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary $t\mapsto a+bt,\ a\geq 0,\,b\in \R,$ by a reflecting Brownian motion.
Marc Yor, P. Salminen
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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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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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Integrable equations associated with the finite‐temperature deformation of the discrete Bessel point process [PDF]
Journal of the London Mathematical Society, 2022 We study the finite‐temperature deformation of the discrete Bessel point process. We show that its largest particle distribution satisfies a reduction of the 2D Toda equation, as well as a discrete version of the integro‐differential Painlevé II equation
M. Cafasso, Giulio Ruzza
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Fractionally integrated Bessel process
Proceedings of the Royal Society A, 2021 We consider a fractionally integrated Bessel process defined by Ysδ,H=∫0∞(uH−(1/2)−(u−s) +H−(1/2))dXuδ, where Xδ is the Bessel process of dimension δ > 2. We discuss the relation of this process to the fractional Brownian motion at its maximum, study the
G. Shevchenko, D. Zatula
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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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Light: Science & Applications, 2023 Bessel beam featured with self-healing is essential to the optical sensing applications in the obstacle scattering environment. Integrated on-chip generation of the Bessel beam outperforms the conventional structure by small size, robustness, and ...
Zihao Zhi +9 more
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