Harnack inequalities for stochastic equations driven by Levy noise

By Feng-Yu Wang, Jian Wang. 2012

57 citations recorded by the source corpus.

Abstract By using coupling argument and regularization approximations of the underlying subordinator, dimension-free Harnack inequalities are established for a class of stochastic equations driven by a Levy noise containing a subordinate Brownian motion. The Harnack inequalities are new even for linear equations driven by Levy noise, and the gradient estimate implied by our log-Harnack inequality considerably generalizes some recent results on gradient estimates and coupling properties derived for Levy processes or linear equations driven by Levy noise. The main results are also extended to semilinear stochastic equations in Hilbert spaces.

Subfields: Applied Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/95f9c31994e2e727448480b8668af691377f830d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Xicheng Zhang
2. Feng-Yu Wang
3. Lihu Xu
4. Michael Röckner
5. Wei Liu
6. Patrick Cattiaux
7. Nathael Gozlan
8. Xing Huang

In Finance

1. Feng-Yu Wang
2. Xicheng Zhang
3. Lihu Xu
4. Michael Röckner
5. Wei Liu
6. Xing Huang
7. Panpan Ren
8. Jianhai Bao

Citations in the corpus

• Gradient estimates for SDEs driven by multiplicative Lévy noise (2013, methodology): “0 such that (see [20, Theorem 1.1]) |∇Ptf| 6 C(p) 1∧t1α (Pt|f|p)1/p, f ∈ B b(R (1.3) d),t > 0. Using this time-change argument and the coupling method, Harnack inequalities are then established in [17]. In this paper, we intend to extend the gradient estimate (1.3) for more general symmetric L´ev”