In characterizing the semistable law, Shimizu reduced the problem to solving the equationH(x)=integral from n=1 to∞(H(x+y)d(μ-ν)(y), x≥0) where μ andτ are given positive measures on [0,∞). In thisnote, we obtai...In characterizing the semistable law, Shimizu reduced the problem to solving the equationH(x)=integral from n=1 to∞(H(x+y)d(μ-ν)(y), x≥0) where μ andτ are given positive measures on [0,∞). In thisnote, we obtain a simple proof and show that some of his conditions can be weakened.展开更多
文摘In characterizing the semistable law, Shimizu reduced the problem to solving the equationH(x)=integral from n=1 to∞(H(x+y)d(μ-ν)(y), x≥0) where μ andτ are given positive measures on [0,∞). In thisnote, we obtain a simple proof and show that some of his conditions can be weakened.
