Approximate local limit theorems with effective rate and application to random walks in random scenery

作者：Giuliano Rita^*; Weber Michel

来源：Bernoulli, 2017, 23(4B): 3268-3310.

DOI：10.3150/16-BEJ846

• Bernoulli part
• effective remainder
• independent random variables
• lattice distributed
• local limit theorem
• random walk in random scenery

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 us to recover Gnedenko and provide a version with effective bounds of Gamkrelidze's local limit theorem. We further establish by this method a local limit theorem with effective remainder for random walks in random scenery.

• 出版日期2017-11