The Wiener–Hopf Equation with Probability Kernel and Submultiplicative Asymptotics of the Inhomogeneous Term

Abstract

We consider the inhomogeneous Wiener–Hopf equation whose kernel is a nonarithmetic probability distribution with positive mean. The inhomogeneous term behaves like a submultiplicative function. We establish asymptotic properties of the solution to which the successive approximations converge. These properties depend on the asymptotics of the submultiplicative function.

Keywords

• Wiener–Hopf equation
• inhomogeneous equation
• nonarithmetic probability distribution
• positive mean
• submultiplicative function
• asymptotic behavior