Geodesic
Davis-type inequalities for a number of diffusion processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 30-43 
Yu. L. Botnikov. Davis-type inequalities for a number of diffusion processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 30-43. http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a1/
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     author = {Yu. L. Botnikov},
     title = {Davis-type inequalities for a~number of diffusion processes},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a1/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this paper we obtain Davis-type maximal inequlaities for Bessel process of dimension parameter $\gg1$ and for the radial Ornstein–Uhlenbeck process. The proofs are based on generalization of the Lenglart domination principle.

[1] A. N. Borodin, P. Salminen, Spravochnik po brounovskomu dvizheniyu, “Lan”, S.-Peterburg, 2000 | Zbl

[2] D. L. Burkholder, “Martingale transforms”, Ann. Math. Statist., 37 (1966), 1494–1504 | DOI | MR | Zbl

[3] B. Davis, “On the integrability of the martingale square function”, Israel J. Math., 8 (1970), 187–190 | DOI | MR | Zbl

[4] A. Göing-Jaeschke, Some generalizations of Bessel processes, Risklab report, 1997

[5] A. Göing-Jaeschke, M. Yor, A survey and some generalizations of Bessel process, Risklab report, 1999

[6] S. E. Graversen, G. Peskir, “Maximal inequalities for the Ornstein–Uhlenbeck process”, Proc. Amer. Math. Soc., 128 (2000), 3035–3041 | DOI | MR | Zbl

[7] S. E. Graversen, G. Peskir, “Maximal inequalities for Bessel processes”, J. Inequal. Appl., 2 (1998), 99–119 | DOI | MR | Zbl

[8] A. Khintchine, “Über dyadische Bruche”, Math. Z., 18 (1923), 109–116 | DOI | MR | Zbl

[9] E. Lenglart, “Relation de domination entre deux processus”, Ann. Inst. Poincaré Probab. Statist., 13 (1977), 171–179 | MR | Zbl

[10] G. Peshkir, A. N. Shiryaev, “Neravenstva Khinchina i martingalnoe rasshirenie sfery ikh deistviya”, Uspekhi mat. nauk, 50:5 (1995), 3–62 | MR | Zbl