Walsh's Brownian Motion-Type of Extensions

Juha Vuolle-Apiala ()
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Juha Vuolle-Apiala: University of Vaasa

Journal of Theoretical Probability, 2001, vol. 14, issue 1, 115-124

Abstract: 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.

Keywords: Markov process; excursion theory; entrance law; rotation invariant; diffusion; Feller process; Walsh's Brownian notion (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1007873115675

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