Geodesic
On global in time existence of solutions to stochastic equations with backward mean derivatives
Journal of computational and engineering mathematics, Tome 5 (2018) no. 4, pp. 64-69.

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

The notion of mean derivatives was introduced by E. Nelson in 60-th years of XX century and at the moment there are a lot of mathematical models of physical and technical processes constructed in terms of equations with those derivatives. The paper is devoted to investigation of stochastic differential equations with backward mean derivatives. This type of equations arise in several models of physical and technical processes and so its investigation is important for applications. But on the other hand, the investigation of such equations requires new methods and ideas. In this paper we deal with the property of global in time existence of all solutions of "inverse" Cauchy problem for equations with backward mean derivatives. A condition that guarantees the global in time existence of such solutions is obtained. This result is useful for many mathematical models of physical and technical processes.
Keywords: backward mean derivatives, stochastic equations, global existence of solutions. 
@article{JCEM_2018_5_4_a5,
     author = {Yu. E. Gliklikh and N. V. Zakharov},
     title = {On global in time existence of solutions to stochastic equations with backward mean derivatives},
     journal = {Journal of computational and engineering mathematics},
     pages = {64--69},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2018_5_4_a5/}
}
TY  - JOUR
AU  - Yu. E. Gliklikh
AU  - N. V. Zakharov
TI  - On global in time existence of solutions to stochastic equations with backward mean derivatives
JO  - Journal of computational and engineering mathematics
PY  - 2018
SP  - 64
EP  - 69
VL  - 5
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCEM_2018_5_4_a5/
LA  - en
ID  - JCEM_2018_5_4_a5
ER  - 
%0 Journal Article
%A Yu. E. Gliklikh
%A N. V. Zakharov
%T On global in time existence of solutions to stochastic equations with backward mean derivatives
%J Journal of computational and engineering mathematics
%D 2018
%P 64-69
%V 5
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCEM_2018_5_4_a5/
%G en
%F JCEM_2018_5_4_a5
Yu. E. Gliklikh; N. V. Zakharov. On global in time existence of solutions to stochastic equations with backward mean derivatives. Journal of computational and engineering mathematics, Tome 5 (2018) no. 4, pp. 64-69. http://geodesic.mathdoc.fr/item/JCEM_2018_5_4_a5/

[1] E. Nelson, “Derivation of the Schrödinger Equation from Newtonian Mechanics”, Physical Review, 150 (1966), 1079–1085 | DOI

[2] E. Nelson, Dynamical Theory of Brownian Motion, Princeton University Press, Princeton, NJ, 1967 | MR

[3] E. Nelson, Quantum Fluctuations, Princeton University Press, Princeton, NJ, 1985 | MR | Zbl

[4] Yu. E. Gliklikh, “Deterministic Viscous Hydrodynamics Via Stochastic Analysis on Groups of Diffeomorphisms”, Methods Funct. Anal. Topology, 9:3 (2003), 146–153 | MR | Zbl

[5] Yu. E. Gliklikh, Global and Stochastic Analysis with Applications to Mathematical Physics, Springer-Verlag, London, 2011 | DOI | MR | Zbl

[6] S. V. Azarina, Yu. E. Gliklikh, “Differential Inclusions with Mean Derivatives”, Dynamic Systems and Applications, 16:1 (2007), 49–71 | MR | Zbl

[7] K. R. Partasarati, Vvedenie v teoriyu veroyatnostei i teoriyu mery, Mir, M., 1988 [K. R. Parthasarathy, Introduction to Probability and Measure, Springer-Verlag, New York, 2005 ] | DOI | MR

[8] K. D. Elworthy, “Stochastic Differential Equations on Manifolds”, Probability Towards 2000, Lecture Notes in Statistics, 128, eds. L. Accardi, C. C. Heyde, Springer, New York, 1998, 165–178 | DOI | MR | Zbl