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Reflecting Diffusions on Lipschitz Domains with Cusps -Analytic Construction and Skorohod Representation-

In: Potential Theory and Degenerate Partial Differential Operators

Author

Listed:
  • Masatoshi Fukushima

    (Osaka University, Department of Mathematical Science, Faculty of Engineering Science)

  • Matsuyo Tomisaki

    (Yamaguchi University, Department of Mathematics, Faculty of Education)

Abstract

The reflecting Brownian motion on a bounded Lipschitz domain D ⊂ R d was constructed by Bass and Hsu [3] as a conservative, symmetric (with respect to the Lebesgue measure) and strong Feller diffusion process (X t ,P x ) on the closure $$ \overline D $$ of D whose transition semigroup on L 2 (D) is associated with the Sobolev space H 1 (D) with inner product 1.1 $$ \varepsilon \left( {u,v} \right) = \frac{1}{2}\int_D {\nabla u \cdot \nabla vdx,} \quad \quad u,v \in {H^1}\left( D \right)$$ .

Suggested Citation

  • Masatoshi Fukushima & Matsuyo Tomisaki, 1995. "Reflecting Diffusions on Lipschitz Domains with Cusps -Analytic Construction and Skorohod Representation-," Springer Books, in: Marco Biroli (ed.), Potential Theory and Degenerate Partial Differential Operators, pages 377-408, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-0085-4_6
    DOI: 10.1007/978-94-011-0085-4_6
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