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

Yu. E. Gliklikh ; E. Yu. Mashkov

Journal of computational and engineering mathematics, Tome 1 (2014) no. 2, pp. 45-51

Résumé

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.

Détail

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