Abstract:
We consider the homogeneous generalized Wiener–Hopf equation
$$
S(x)=\int^x_{-\infty}S(x-y)F(dy),\qquad x\ge0,
$$
wehere $F$ is a probability distribution on $\mathbb R$ with zero mean, finite variance, and infinite moment $\int^\infty_0x^3F(dy)$. Its $P^*$-solution $S(x)$ enjoys the property
$$
S(x)-ax\sim b\int^x_0\int^\infty_y\int^\infty_vF((u,\infty))\,dudvdy\qquad\text{as}\quad x\to\infty,
$$
where $a$ and $b$ are explicit positive constants.
Fulltext:
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