Stochastic Differential Equations Driven by Stable Processes for Which Pathwise Uniqueness Fails
نویسندگان
چکیده
Let Zt be a one-dimensional symmetric stable process of order α with α ∈ (0, 2) and consider the stochastic differential equation dXt = φ(Xt−)dZt. For β < 1 α ∧ 1, we show there exists a function φ that is bounded above and below by positive constants and which is Hölder continuous of order β but for which pathwise uniqueness of the stochastic differential equation does not hold. This result is sharp. AMS 2000 Mathematics Subject Classification: Primary 60H10, Secondary 60G52.
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