A Gaussian Oscillator

Krzysztof Burdzy (University of Washington)
David White (University of Washington)

Abstract


We present a stochastic process with sawtooth paths whose distribution is given by a simple rule and whose stationary distribution is Gaussian. The process arose in a natural way in research on interaction of an inert particle with a Brownian particle.

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Pages: 92-95

Publication Date: October 6, 2004

DOI: 10.1214/ECP.v9-1113

References

  1. S. Ethier and T. Kurtz Markov processes. Characterization and convergence. John Wiley and Sons, Inc., New York, 1986. Math. Review 88a:60130
  2. F. Knight, On the path of an inert object impinged on one side by a Brownian particle. Probab. Theory Related Fields 121, (2001) 577-598. Math. Review 2002i:60148
  3. D. White, Processes with inert drift. Ph.D. Thesis, University of Washington (forthcoming)


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