Regularity of Harmonic functions for a class of singular stable-like processes

By Richard F. Bass, Zhen-Qing Chen. 2009

51 citations recorded by the source corpus.

AbstractWe consider the system of stochastic differential equations $$ dX_t=A(X_{t-})\, dZ_t, $$where Zt1 , . . . , Zdt are independent one-dimensional symmetric stable processes of order α, and the matrix-valued function A is bounded, continuous and everywhere non-degenerate. We show that bounded harmonic functions associated with X are Hölder continuous, but a Harnack inequality need not hold. The Lévy measure associated with the vector-valued process Z is highly singular.

Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/88df933163b3e44931f38d17e0309c411388bfaf

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In Computational Theory and Mathematics

1. Xavier Ros-Oton
2. J. Serra
3. Nicola Garofalo
4. Enrico Valdinoci
5. Mahamadi Warma
6. Raffaella Servadei
7. Lexing Ying
8. Victor Minden

In Finance

1. Xavier Ros-Oton
2. J. Serra
3. Nicola Abatangelo

In Mathematical Physics

1. Xavier Ros-Oton
2. J. Serra
3. Xavier Fernández-Real
4. Lexing Ying
5. Victor Minden
6. Van Hoang Nguyen

Citations in the corpus

• Regularity theory for general stable operators (2014, background): “1), or related ones, has been widely investigated; see the works by Bass, Kassmann, Schwab, Silvestre, Sztonyk, and Bogdan, among others [1, 23, 22, 3, 39, 21, 2, 37, 5, 6, 7, 9, 24].”