Abstract:
We prove the existence of a solution to the inhomogeneous Wiener–Hopf equation whose kernel is a probability distribution generating a random walk drifting to $-\infty$. Asymptotic properties of a solution are found depending on the corresponding properties of the free term and the kernel of the equation.
Keywords:integral equation, inhomogeneous equation, inhomogeneous generalized Wiener–Hopf equation, probability distribution, drift to minus infinity, asymptotic behavior.
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