Long memory and self-similar processes
This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.
Weak quenched limiting distributions for transient one-dimensional random walk in a random environment
We consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter that determines the fluctuations of the process. When , the averaged distributions of the hitting times of the random walk converge to a -stable distribution. However, it was shown recently that in this case there does not exist a quenched limiting distribution of the hitting times. That is, it is not true that for...
Optimal and near-optimal () inventory policies for Levy demand processes
Optimal and Near-Optimal () Inventory Policies for Levy Demand Processes
is a continuous-time, real-valued stochastic process which has independent and stationary increments, with no Brownian component. We study some of the fundamental properties of Levy jump processes and develop inventory models for them. Of particular interest to us is the gamma-distributed Levy process, in which the demand that occurs in a fixed period of time has a gamma distribution. We study the relevant properties of these processes, and we develop a quadratically convergent...
Sample correlations of infinite variance time series models: An empirical and theoretical study.
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