Abstract
This paper is concerned with the fundamental properties of the response of relay-type scalar stochastic systems. The system considered here is described by scalar Ito's stochastic differential equation, in which the diffusion coefficient is assumed to be twice continuously differentialable, and the drift coefficient is assumed to have negative jumps in some points and to be twice continuously differentialable in other points. It is well-known fact that the Fokker-Planck equation for the probability density function for the response does not hold on the whole domain of the state space, but its equation holds on each domain of the state space in which the drift coefficients are differentialable.
Firstly, the existence, uniqueness, Markov nature and continuity of the solution for the relay-type scalar stochastic differential equation are discussed, and secondly the boundary conditions to solve the Fokker-Planck equations on each domain of the state space are obtained.
