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.