On the probability distribution of the ranks in the symmetric random walk process
Document Type
Conference Proceeding
Publication Date
12-1-2003
Abstract
We consider a discrete-time random walk process, in which the successive increments are i.i.d. random variables from a symmetric continuous distribution with mean zero. For the random walk process of n observations, we not only prove the arc-sine law in a different way, but also explicitly compute the probabilities that the jth observation in the sequence will have a certain rank i among all n observations. Some of the directions for possible applications include extending the result to the sequential selection strategy for the random walk process and deriving the rank probability distribution for a more general stochastic process.
Publication Source (Journal or Book title)
Proceedings Annual Meeting of the Decision Sciences Institute
First Page
2393
Last Page
2398
Recommended Citation
Chun, Y. (2003). On the probability distribution of the ranks in the symmetric random walk process. Proceedings Annual Meeting of the Decision Sciences Institute, 2393-2398. Retrieved from https://repository.lsu.edu/infosys_pubs/72