On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise

Alexei M. Kulik

Stochastic Processes and their Applications, 2019, vol. 129, issue 2, 473-506

Abstract: For an SDE driven by a rotationally invariant α-stable noise we prove weak uniqueness of the solution under the balance condition α+γ>1, where γ denotes the Hölder index of the drift coefficient. We prove the existence and continuity of the transition probability density of the corresponding Markov process and give a representation of this density with an explicitly given “principal part”, and a “residual part” which possesses an upper bound. Similar representation is also provided for the derivative of the transition probability density w.r.t. the time variable.

Keywords: SDE; Martingale problem; Transition probability density; Parametrix method; Approximate fundamental solution; Approximate harmonic function (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2018.03.010

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