A case of a random difference equation connected with a filtered binary process
The author studies the triggered shot noise process by using the random difference equation \[ Y_{n+ 1}= X_{n+ 1}(1- Y_n),\qquad n= 1, 2,\dots,\tag{1} \] where \(Y_1= X_1\) and the \(X_i\) are independent real random variables with the same distribution. In the present paper, there was given a complete numerical study of the stationary distribution of \(Y_n\) in (1) for the distribution of \(X_n\) given by \[ g_X(x)= a^2(- \text{Log }x) x^{a- 1} \text{\textbf{1}}_{]0, 1[}(x) dx \] for the particular case \(a= 1/2\). Remember that in 1986-1989 \textit{R. F. Pawula} and \textit{S. O. Rice} presented in their various papers a study of the random telegraph signal with filtering by the equation (1).
scientific article; zbMATH DE number 885465