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On Sojourn Distributions of Processes Related to Some Higher-Order Heat-Type Equations

Author

Listed:
  • Y. Nikitin

    (State University of St. Petersburg)

  • E. Orsingher

    (Universit'a di Roma “La Sapienza”)

Abstract

It is well known that the sojourn time of Brownian motion B(t), t>0 on the positive half-line, during the interval [0, t] and under the condition B(t)=0, is uniformly distributed, while it has the form of the “corrected arc-sine law” when the condition B(t)>0 is assumed. We find the analogues of these laws for “processes” X(t), t>0 governed by signed measures whose densities are the fundamental solutions of third and fourth-order heat-type equations. Surprisingly, both laws hold for the fourth-order “process.” The uniform law is still valid for the third-order “process” but a different law emerges when the condition X(t)>0 is considered.

Suggested Citation

  • Y. Nikitin & E. Orsingher, 2000. "On Sojourn Distributions of Processes Related to Some Higher-Order Heat-Type Equations," Journal of Theoretical Probability, Springer, vol. 13(4), pages 997-1012, October.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:4:d:10.1023_a:1007861923910
    DOI: 10.1023/A:1007861923910
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    References listed on IDEAS

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    1. Hochberg, Kenneth J. & Orsingher, Enzo, 1994. "The arc-sine law and its analogs for processes governed by signed and complex measures," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 273-292, August.
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