Stochastic Leontieff type equations with non-constant coefficients

Abstract

Leontieff type equation is a differential-algebraic equation arising, in particular, in description of dynamically distorted signal in a radio device. In investigation of the signals, it is necessary to take into account noise that requires consideration of stochastic version of Leontieff type equations. For those equations, we apply the machinery of the so-called Nelson’s mean derivatives (more exactly, symmetric mean derivatives that is a natural analogue of physical velocity of deterministic processes) and obtain formulae of solutions in the case of non-constant coefficients of equations.

Keywords:

• stochastic Leontieff type equations
• non-constant coefficints
• mean derivatives

AMS Subject Classifications:

• 34A09
• 34A12
• 60H10
• 60H30

Acknowledgements

 

Notes

The research is supported in part by RFBR Grants 12-01-00183-a and 13-01-00041-a.