Geodesic
Stochastic Leontieff type equations in terms of current velocities of the solution
Journal of computational and engineering mathematics, Tome 1 (2014) no. 2, pp. 45-51.

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

In papers by A.L. Shestakov and G.A. Sviridyuk [1, 2] a new model of the description of dynamically distorted signals in some radio devises is suggested. In [3, 4] the influence of noise is taken into account in terms of the so-called current velocities of the Wiener process instead of using white noise. This allows the authors to avoid using the generalized function. It should be pointed out that by physical meaning the current velocity is a direct analog of physical velocity for the determinitic processes. Note that the use of current velocity of the Wiener process means that in the construction of mean derivatives the $\sigma$-algebra "present" for the Wiener process is under consideration while there is another possibility to deal with the "present" $\sigma$-algebra of the solution as it is in the usual case in the theory of stochastic differential equation with mean derivatives. In this paper we consider stochastic Leontiev type equation of some special sort given in terms of current velocities of the solution and obtain existence of solution theorem as well as some formulae for the density of the solution.
Keywords: mean derivatives, current velocities, stochastic Leontieff type equations. 
@article{JCEM_2014_1_2_a4,
     author = {Yu. E. Gliklikh and E. Yu. Mashkov},
     title = {Stochastic {Leontieff} type equations in terms of current velocities of the solution},
     journal = {Journal of computational and engineering mathematics},
     pages = {45--51},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2014_1_2_a4/}
}
TY  - JOUR
AU  - Yu. E. Gliklikh
AU  - E. Yu. Mashkov
TI  - Stochastic Leontieff type equations in terms of current velocities of the solution
JO  - Journal of computational and engineering mathematics
PY  - 2014
SP  - 45
EP  - 51
VL  - 1
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCEM_2014_1_2_a4/
LA  - en
ID  - JCEM_2014_1_2_a4
ER  - 
%0 Journal Article
%A Yu. E. Gliklikh
%A E. Yu. Mashkov
%T Stochastic Leontieff type equations in terms of current velocities of the solution
%J Journal of computational and engineering mathematics
%D 2014
%P 45-51
%V 1
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCEM_2014_1_2_a4/
%G en
%F JCEM_2014_1_2_a4
Yu. E. Gliklikh; E. Yu. Mashkov. Stochastic Leontieff type equations in terms of current velocities of the solution. Journal of computational and engineering mathematics, Tome 1 (2014) no. 2, pp. 45-51. http://geodesic.mathdoc.fr/item/JCEM_2014_1_2_a4/

[1] A. L. Shestakov, G. A. Sviridyuk, “A new approach to measurement of dynamically perturbed signals”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2010, no. 5, 116–120 | Zbl

[2] A. L. Shestakov, G. A. Sviridyuk, “Optimal measurement of dynamically distorted signals”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2011, no. 8, 70–75 | Zbl

[3] A. L. Shestakov, G. A. Sviridyuk, “On the Measurement of the «White Noise»”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, no. 13, 99–108 | Zbl

[4] Yu. E. Gliklikh, E. Yu. Mashkov, “Stochastic Leontieff type equations and mean derivatives of stochastic processes”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:2 (2013), 25–39 | Zbl

[5] E. Nelson, “Derivation of the Schrödinger Equation from Newtonian Mechanics”, Physical Reviews, 6 (1979), 1079–1085

[6] E. Nelson, Dynamical Theory of Brownian Motion, Princeton University Press, Princeton, 1967, 142 pp. | MR

[7] E. Nelson, Quantum Fluctuations, Princeton University Press, Princeton, 1985, 147 pp. | MR | Zbl

[8] S. V. Azarina, Yu. E. Gliklikh, “Differential inclusions with mean derivatives”, Dynamic systems and applications, 16 (2007), 49–72 | MR

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

[10] V. F. Chistyakov, A. A. Scheglova, Izbrannye glavy teorii algebro-differentsialnykh sistem, Nauka, Novosibirsk, 2003, 319 pp. | MR

[11] F. R. Gantmakher, Teoriya matrits, Nauka, Moskva, 1966, 576 pp. | MR