Approximate Local Limit Theorems with Effective Rate and Application to Random Walks in Random Scenery
Approximate Local Limit Theorems with Effective Rate and Application to Random Walks in Random Scenery
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具有有效率的近似局部极限定理及其在随机场景中随机游走的应用
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Michel J. G. Weber
中科院分区：
文献类型：
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作者：
R. Giuliano;Michel J. G. Weber
证明了用Bernoulli部分提取方法可以得到具有有效误差项的独立格值随机变量和的局部极限定理的近似形式，即具有显式参数和普适常数.我们还证明了我们的估计允许恢复Gnedenko和Gamkrelidze局部极限定理。利用这一方法，我们进一步建立了随机景物中随机游动的一个带有效余数的局部极限定理。
We show that the Bernoulli part extraction method can be used to obtain approximate forms of the local limit theorem for sums of independent lattice valued random variables, with effective error term, that is with explicit parameters and universal constants. We also show that our estimates allow to recover Gnedenko and Gamkrelidze local limit theorems. We further establish by this method a local limit theorem with effective remainder for random walks in random scenery.