On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise
By A. Kulik. Stochastic Processes and their Applications, 2015
55 citations recorded by the source corpus.
For an SDE driven by a rotationally invariant $\alpha$-stable noise we prove weak uniqueness of the solution under the balance condition $\alpha+\gamma>1$, where $\gamma$ denotes the Holder index of the drift coefficient. We prove 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.
Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0e96b17ce59a531a41ca5daa051a3b3cc7406f28
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
In Finance
In Mathematical Physics
Citations in the corpus
- Strong convergence of the Euler–Maruyama approximation for a class of Lévy-driven SDEs (2017, background): “For instance, if (Lt)t≥0 is an isotropic α-stable Lévy process, then the SDE dXt = b(Xt−) dt+ dLt fails, in general, to have a pathwise unique solution if b is β-Hölder continuous with β + α < 1, cf. [28]; recently, Kulik [16] has shown that the SDE admits a pathwise unique solution if β + α > 1.”