We consider the discrete Wiener-Hopf equation with inhomogeneous term $$g = \{ {g_j}\} _{j = 0}^\infty \in {l_\infty }$$ g = { g j } j = 0 ∞ ∈ l ∞ ; the kernel of the equation is an arithmetic probability distribution generating a random walk drifting to +∞. We prove that the previously obtained formula for the Wiener-Hopf equation with general arithmetic kernel for g ∈ l 1 is a solution to the equation for g ∈ l ∞ 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 ∈ l 1 ; (2) g ∈ l ∞ ; (3) g j → const as j → ∞; (4) g ∉ l 1 and g j ↓ 0 as j → ∞.

中文翻译：

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核为正漂移概率分布的离散 Wiener-Hopf 方程

我们考虑具有非齐次项的离散 Wiener-Hopf 方程 $$g = \{ {g_j}\} _{j = 0}^\infty \in {l_\infty }$$ g = { gj } j = 0 ∞ ∈ ∞ ; 方程的核心是一个算术概率分布，产生一个漂移到 +∞ 的随机游走。我们证明了先前获得的具有 g ∈ l 1 的通用算术核的 Wiener-Hopf 方程的公式是 g ∈ l ∞ 方程的解，并且逐次逼近收敛于该解。考虑到它们的特殊性，在下列情况下建立解的渐近性： (1) g ∈ l 1 ；(2) g ∈ l ∞ ；(3) gj → const as j → ∞；(4) g ∉ l 1 和 gj ↓ 0 为 j → ∞。