Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 1, 1-9

OSCILLATIONS IN RANDOM WALKS

By

DAVID BRANSON, University of Essex, Colchester

SUMMARY. Some probability distributions associated with the number of oscillations in continuous symmetric random walks are derived by elementary combinatorial arguments. A connection is established with the number of forward and backward records in the sequence of random-walk step lengths .

 

AMS (1991) subject classification. 60C05, 11B73, 60G50.

Key words and phrases. Random walk, oscillations, Stirling numbers, records.

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