Geodesic
The second order local time of the Bessel process at the moment inverse to local time
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 34, Tome 525 (2023), pp. 30-50
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According to the Ray–Knight description the Bessel local time at the moment inverse to local time is a diffusion process with respect to space parameter. This diffusion has a local time. Thus, we come to the definition of the local time of the original Bessel local time. We will call such a process the Bessel local time of the second order at the moment, inverse to local time. The paper studies the Laplace transform of the distribution of the second order Bessel local time. 
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A. N. Borodin. The second order local time of the Bessel process at the moment inverse to local time. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 34, Tome 525 (2023), pp. 30-50. http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a3/

[1] A. N. Borodin, “Brounovskoe lokalnoe vremya vtorogo poryadka”, Zap. nauchn. semin. POMI, 505, 2021, 75–86

[2] A. N. Borodin, “Brounovskoe lokalnoe vremya vtorogo poryadka v moment, obratnyi k lokalnomu vremeni”, Zap. nauchn. semin. POMI, 510, 2022, 51–64

[3] F. B. Knight, “Random walks and a sojourn density process of Brownian motion”, Trans. Amer. Math. Soc., 109 (1963), 56–86

[4] D. B. Ray, “Sojourn times of a diffusion process”, Ill. J. Math., 7 (1963), 615–630

[5] A. N. Borodin, Sluchainye protsessy, Lan, Sankt-Peterburg, 2017

[6] A. N. Borodin, On the distribution of functionals of Brownian local time, LOMI Preprints E–4–85, L., 1985

[7] A. N. Borodin, P. Salminen, Spravochnik po brounovskomu dvizheniyu. Fakty i formuly, Lan, Sankt-Peterburg, 2016

[8] I. Karatzas, S. E. Shreve, Brovnian Motion and Stochastic Calculus, 2-nd ed., Springer, Berlin–Heidelberg–New York, 1991