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Walsh's Brownian Motion-Type of Extensions

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  • Juha Vuolle-Apiala

    (University of Vaasa)

Abstract

Let (X t ) be a rotation invariant Feller process on the state space F ∈ R2{} consisting of finite number of rays, meeting at 0. We study a certain class of possible strong Markov extensions of (X t ) to F ∪ ,{} given the corresponding radial extension to [0, ∞). A well-known example is the class of “Walsh's Brownian motions,” in the case where (X t ) is the Brownian motion on F. It turns out that while the symmetric extension of “Walsh's Brownian motion-type” always exists, the non-symmetric extension exists iff (X t ), roughly speaking, does not jump from one ray to another before hitting 0.

Suggested Citation

  • Juha Vuolle-Apiala, 2001. "Walsh's Brownian Motion-Type of Extensions," Journal of Theoretical Probability, Springer, vol. 14(1), pages 115-124, January.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:1:d:10.1023_a:1007873115675
    DOI: 10.1023/A:1007873115675
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    Cited by:

    1. Juha Vuolle-Apiala, 2003. "On Certain Extensions of a Rotation Invariant Markov Process," Journal of Theoretical Probability, Springer, vol. 16(4), pages 957-969, October.

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