# Tag Info

Accepted

### Local probabilities for lattice random walk

For the one dimensional case, a quite nice bound is in Theorem 4.2 of [1]. See also [2]. The dependence on $\epsilon$ that you seek was first shown by Kesten[3]. The combinatorial approach was ...
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1 vote
Accepted

### Bernoulli trials with small dependencies: asymptotics (central limit theorem, law of the iterated logarithm)

For $0<\beta \le 1/2$, any limiting distribution of the rescaled process $S_n/n^\beta$ will be fully supported in $[-1,1]$, so it will not be normal. The downward drift will imply (using Hoeffding'...
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Accepted

### Invariance principle: Brownian bridge and random walk conditioned on end point

A more general theorem is proved in [1] for the limits of random walks in the domain of attraction of a stable law. In the case described in the problem, one can also use the strong approximation ...
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