In the present paper the solutions of two integral equations are derived. One of the integral equations dominates the mathematical description of the stochastic process {v n , n = 1,2, …}, recursively defined by K is a positive constant, τ 1, τ 2, …; Σ 1, Σ 2, …; are independent, non-negative variables, with τ 1, τ 2,…, identically distributed, similarly, the variables Σ 1, Σ 2, …, are identically distributed.