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Markov Averaging

In: Applied Mathematics

Author

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  • Gerald Dennis Mahan

    (Pennsylvania State University)

Abstract

Markov refers to a type of statistical averaging that is widely used for many different kinds of problems. The easiest problem is to have a particle moving in one dimension with a random walk. Then one can calculate the probabilityp N (x) that the particle has moved a distancex after N steps. Alternately, the other particles may exert a force F on the central particle, depending upon the positions of these other particles. Then one might try to calculate the probability p N (F) of having the forceF if there areN other particles. The central theme of these problems, defines the average as being Markovian, is that the other particles act independently of each other. Similarly, in the random walk, each step proceeds independently of any earlier or later step. This chapter will give three examples of Markov averaging for several different problems. Three are chosen to give different final distributions: Gaussian, exponential, and Lorentzian. The main ideas are contained in a review article by Chandrasekhyar (1).

Suggested Citation

  • Gerald Dennis Mahan, 2002. "Markov Averaging," Springer Books, in: Applied Mathematics, chapter 7, pages 177-194, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-1315-5_7
    DOI: 10.1007/978-1-4615-1315-5_7
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