Stochastic Leontieff type equations in terms of current velocities of the solution~II

Yu. E. Gliklikh ; E. Yu. Mashkov

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 3, pp. 31-40

Résumé

In papers by A.L. Shestakov and G.A. Sviridyuk a new model of the description of dynamically distorted signals in some radio devices is suggested in terms of so-called Leontieff type equations (a particular case of algebraic-differential equations). In that model the influence of noise is taken into account in terms of the so-called symmetric mean derivatives 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 deterministic 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 also another possibility: to deal with the $\sigma$-algebra "present" of the solution as it is usually done in the theory of stochastic differential equation with mean derivatives. This approach was previously suggested by the authors under the assumption that the matrix pencil, that determines the equation, satisfies the so-called "rank-degree" condition. In this paper we consider stochastic Leontieff type equation given in terms of current velocities of the solution without this assumption.

Détail

Keywords: mean derivatives; current velocities; stochastic Leontieff type equations.