Wiener–Hopf equation whose kernel is a probability distribution

Resumo

We prove the existence of a solution of an inhomogeneous generalized Wiener–Hopf equation whose kernel is a probability distribution on R generating a random walk drifting to +∞, while the inhomogeneous term f of the equation belongs to the space L₁(0,∞) or L_∞(0,∞). We establish the asymptotic properties of the solution of this equation under various assumptions about the inhomogeneity f.