THEOREMS ON CONVERGENCE OF STOCHASTIC INTEGRALS DISTRIBUTIONS TO SIGNED MEASURES AND LOCAL LIMIT THEOREMS FOR LARGE DEVIATIONS

N. V. Smorodina; M. M. Faddeev

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THEOREMS ON CONVERGENCE OF STOCHASTIC INTEGRALS DISTRIBUTIONS TO SIGNED MEASURES AND LOCAL LIMIT THEOREMS FOR LARGE DEVIATIONS

机译：随机积分分布到有符号度量的收敛定理和大偏差的局部极限定理

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We study properties of symmetric stable measures with index α > 2, α ≠ 2m, m ∈ N. Such measures are signed ones, and hence they are not probability measures. For this class of measures, we construct an analogue of the Levy-Khinchin representation. We show that, in some sense, these signed measures are limit measures for sums of independent random variables.

机译：我们研究索引为α> 2，α≠2m，m∈N的对称稳定测度的性质。此类测度是有符号测度，因此不是概率测度。对于此类措施，我们构建了Levy-Khinchin表示的类似物。我们表明，从某种意义上说，这些有符号测度是对独立随机变量总和的极限测度。

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来源
《Journal of Mathematical Sciences》 |2010年第4期|P.550-565|共16页
作者
N. V. Smorodina; M. M. Faddeev;
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作者单位

St.Petersburg State University, St.Petersburg, Russia;

rnSt.Petersburg State University, St.Petersburg, Russia;

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THEOREMS ON CONVERGENCE OF STOCHASTIC INTEGRALS DISTRIBUTIONS TO SIGNED MEASURES AND LOCAL LIMIT THEOREMS FOR LARGE DEVIATIONS

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