Abstract:
We consider the discrete Wiener–Hopf equation with inhomogeneous term $g=\{g_j\}_{j=0}^{\infty} \in\nobreak l_\infty$; the kernel of the equation is an arithmetic probability distribution generating a random walk drifting to $+\infty$. We prove that the previously obtained formula for the Wiener–Hopf equation with general arithmetic kernel for $g \in l_1$ is a solution to the equation for $g \in l_\infty$ and that successive approximations converge to the solution. The asymptotics of the solution is established in the following cases with account taken of their peculiarities: (1) $g \in l_1$; (2) $g \in l_\infty$; (3) $g_j\to \text{const}$ as $j\to\infty$; (4) $g \not\in l_1$ and $g_j\downarrow 0$ as $j\to\infty$.
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