Uniqueness of stable processes with drift
By Zhen-Qing Chen, Longmin Wang. 2013
57 citations recorded by the source corpus.
Suppose that d ≥ 1 and α ∈ (1, 2). Let Y be a rotationally symmetric α-stable process on R d and b a R-valued measurable function on R belonging to a certain Kato class of Y . We show that dX t = dYt + b(X b t )dt with X b 0 = x has a unique weak solution for every x ∈ R. Let Lb = −(−∆)α/2 + b · ∇, which is the infinitesimal generator of X. Denote by C∞ c (R) the space of smooth functions on R with compact support. We further show that the martingale problem for (Lb, C∞ c (R)) has a unique solution for each initial value x ∈ R. AMS 2010 Mathematics Subject Classification: Primary 60H10, 47G20; Secondary 60G52
Subfields: Finance, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ea00ffca7303ffc0bc16b8d120dab0a938d8f3d2
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Citations in the corpus
- Stable process with singular drift (2014, background): “As remarked in [10], our Theorem 1.4 does not cover these results in [10].”
- Parametrix construction of the transition probability density of the solution to an SDE driven by $\alpha$-stable noise (2014, methodology): “See also [9], where alternatively the martingale problem approach was used.”
- Heat kernels for non-symmetric diffusion operators with jumps (2016, background): “[25] J.-M. Wang.”
- Stochastic flows for Lévy processes with Hölder drifts (2015, background): “We thank Zenghu Li, Feng-Yu Wang and Jian Wang for helpful discussions, and Enrico Priola for communications about his Remark 5.5 of [18].”