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.
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