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Pitman's 2M-X Theorem for Skip-Free Random Walks with Markovian Increments
Pitman's representation three-dimensional Bessel process telegrapher s equation queue Burke's theorem
2009/5/4
Let $(xi_k, kge 0)$ be a Markov chain on ${-1,+1}$ with $xi_0=1$ and transition probabilities $P(xi_{k+1}=1| xi_k=1)=a>b=P(xi_{k+1}=-1| xi_k=-1)$. Set $X_0=0$, $X_n=xi_1+cdots +xi_n$ and $M_n=max_{0le...
A Log-scale Limit Theorem for One-dimensional Random Walks in Random Environments
RWRE limit theorems branching large deviations
2009/4/27
We consider a transient one-dimensional random walk X_n in random environment having zero asymptotic speed. For a class of non-i.i.d. environments we show that log X_n / log n converges in probability...