The Discrete Wiener-Hopf Equation with Probability Kernel of Oscillating Type
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We prove the existence of a solution to the discrete inhomogeneous Wiener-Hopf equation whose kernel is an arithmetic probability distribution generating an oscillating random walk. Asymptotic properties of the solution are established depending on the properties of the inhomogeneous term of the equation and its kernel.
Keywordsdiscrete Wiener-Hopf equation inhomogeneous equation asymptotic behavior arithmetic distribution oscillating type
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