On refinements of neo-classical inequality and its applications to stochastic differential equations and Brownian motion
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 257-265.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this article some estimates are refined for the best constant in the well-known so called neo-classical inequality, which is the generalization of the Newton binomial formula in terms of Wright — Fox functions. The results of this article are applied to stochastic differential equations, Brownian motion and estimates of probability distributions.
Keywords: neo-classical inequality, stochastic differential inequality, Wright — Fox function, Berry — Essen inequality, Meller — König — Zeller operators.
@article{CHFMJ_2017_2_3_a0,
     author = {D. S. Donchev and S. M. Sitnik and E. L. Shishkina},
     title = {On refinements of neo-classical inequality and its applications to stochastic differential equations and {Brownian} motion},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {257--265},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a0/}
}
TY  - JOUR
AU  - D. S. Donchev
AU  - S. M. Sitnik
AU  - E. L. Shishkina
TI  - On refinements of neo-classical inequality and its applications to stochastic differential equations and Brownian motion
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2017
SP  - 257
EP  - 265
VL  - 2
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a0/
LA  - ru
ID  - CHFMJ_2017_2_3_a0
ER  - 
%0 Journal Article
%A D. S. Donchev
%A S. M. Sitnik
%A E. L. Shishkina
%T On refinements of neo-classical inequality and its applications to stochastic differential equations and Brownian motion
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2017
%P 257-265
%V 2
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a0/
%G ru
%F CHFMJ_2017_2_3_a0
D. S. Donchev; S. M. Sitnik; E. L. Shishkina. On refinements of neo-classical inequality and its applications to stochastic differential equations and Brownian motion. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 257-265. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a0/

[1] T. Lyons, “Differential equations driven by rough signals”, Revista Matematica Iberoamericana, 14:2 (1998), 215–310 | DOI | MR | Zbl

[2] Y. S. Chow, H. Teicher, Probability Theory, Springer-Verlag, New York, 1988, 455 pp. | MR | Zbl

[3] E. R. Love, G. Prasad, A. Sahai, “An improved estimate of the rate of the integrated Meyer — König and Zeller operators for functions of bounded variation”, Journal of Mathematical Analysis and Applications, 187:1 (1994), 1–16 | DOI | MR | Zbl

[4] E. R. Love, “On an inequality conjectured by T. J. Lyons”, Journal of Inequalities and Applications, 2 (1998), 229–233 | MR | Zbl

[5] E. R. Love, “An inequality conjectured by T. J. Lyons”, Integral Transforms and Special Functions, 10:3–4 (2000), 283–288 | DOI | MR | Zbl

[6] J.-H. Li, On Lyons' inequality and estimates of convergence rates of approximation via Meyer — König and Zeller operators, Master thesis, National Central University, 2004

[7] S.M. Sitnik, “On generalization of binomial theorem which arising in differential equations theory”, Bulletin of Voronezh Institute of MVD, 2004, no. 1, 143–147 (In Russ.)

[8] K. Hara, M. Hino, Fractional order Taylor's series and the neo-classical inequality, 2010, 11 pp., arXiv: 1001.1775v1 | MR

[9] R. N. Bhattacharya, R. R. Rao, Normal approximation and asymptotic expansions, Society for Industrial and Applied Mathematics, Philadelphia, 2010, 316 pp. | MR | Zbl

[10] H. M. Srivastava, H. L. Manocha, A treatise on generating functions, Halsted Press, New York, 1984, 569 pp. | MR | Zbl

[11] R. Gorenflo [et al.], Mittag-Leffler Functions, Related Topics and Applications, Springer, Berlin, 2014, 443 pp. | MR | Zbl

[12] D. Donchev, S. Rachev, D. Steigerwald, “Optimal policies for investment with time-varying return probabilities”, Journal of Computational Analysis and Applications, 4 (2002), 269–312 | DOI | MR | Zbl

[13] D. Donchev, “An excursion characterization of the first hitting time of Brownian motion in a smooth boundary”, Journal of Random Operators and Stochastic Equations, 15 (2007), 35–48 | MR | Zbl

[14] D. Donchev, “Random series with time-varying discounting”, Communications in Statistics — Theory and Methods, 40:16 (2011), 2866–2878 | DOI | MR | Zbl

[15] D. Donchev, “Exit probability levels of diffusion processes”, Proceedings of the American Mathematical Society, 145:5 (2017), 2241–2253 | DOI | MR | Zbl

[16] D. Donchev , S. M. Sitnik , E. L. Shishkina, “On generalization of binomial theorem arising in stochastic differential equations theory”, Bulletin of Applied Mathematics, Informatics and Mechanics Faculty of Voronezh State University, 15 (2017), 33–42 (In Russ.)

[17] F. Qi, “Bounds for the ratio of two Gamma functions”, Journal of Inequalities and Applications, 2010, 493058, 84 | MR

[18] S. M. Sitnik, “Refinements and generalizations of classical inequalities”, Mathematical forum. Results of science. South of Russia, 3 (2009), 221–266 (In Russ.)

[19] S. M. Sitnik, Generalized Young and Cauchy — Bunyakowsky inequalities with applications: a survey, 2010, 51 pp., arXiv: 1012.3864

[20] T. Rado, “On convex functions”, Transactions of American Mathematical Society, 37 (1935), 266–285 | DOI | MR