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

Richard F. Bass; Zhen Qing Chen

doi:10.1007/s00209-009-0581-0

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

Richard F. Bass, Zhen Qing Chen^*

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

30 引用（Scopus）

摘要

We consider the system of stochastic differential equations dX_t = A(X_t-)dZ_t, where Z_t¹, . . . , Z_t^d 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.

源语言	英语
页（从-至）	489-503
页数	15
期刊	Mathematische Zeitschrift
卷	266
期	3
DOI	https://doi.org/10.1007/s00209-009-0581-0
出版状态	已出版 - 2010
已对外发布	是

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Bass, R. F., & Chen, Z. Q. (2010). Regularity of Harmonic functions for a class of singular stable-like processes. Mathematische Zeitschrift, 266(3), 489-503. https://doi.org/10.1007/s00209-009-0581-0

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keywords = "Harmonic function, Harnack inequality, H{\"o}lder continuity, Krylov-Safonov technique, Pseudo-differential operator, Stable-like process, Support theorem",

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AU - Bass, Richard F.

AU - Chen, Zhen Qing

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N2 - We consider the system of stochastic differential equations dXt = A(Xt-)dZt, where Zt1, . . . , Ztd 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.

AB - We consider the system of stochastic differential equations dXt = A(Xt-)dZt, where Zt1, . . . , Ztd 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.

KW - Harmonic function

KW - Harnack inequality

KW - Hölder continuity

KW - Krylov-Safonov technique

KW - Pseudo-differential operator

KW - Stable-like process

KW - Support theorem

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VL - 266

SP - 489

EP - 503

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3

ER -

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

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