Coupling property and gradient estimates of L\'{e}vy processes via the symbol
By René L. Schilling, Paweł Sztonyk, Jian Wang. 2010
85 citations recorded by the source corpus.
We derive explicitly the coupling property for the transition semigroup of a L\'{e}vy process and gradient estimates for the associated semigroup of transition operators. This is based on the asymptotic behaviour of the symbol or the characteristic exponent near zero and infinity, respectively. Our results can be applied to a large class of L\'{e}vy processes, including stable L\'{e}vy processes, layered stable processes, tempered stable processes and relativistic stable processes.
Subfields: Applied Mathematics, Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/cc0567d96abac983a4ef2f12e259ec2ebfdb1b75
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
In Finance
In Management Science and Operations Research
Citations in the corpus
- Gradient estimates for SDEs driven by multiplicative Lévy noise (2013, methodology): “en bt(x) = Ax for a matrix A and σt(x) = Id, the gradient estimate of type |∇Ptf| 6kfk∞ϕ(t), t > 0, f ∈ Bb(Rd) has been derived in [13] by using lower bound conditions of the L´evy measure, and in [10] for A = 0 by using asymptotic behaviours of the symbol of Lt; see also [15] for a derivative fo”
- Strong convergence of the Euler–Maruyama approximation for a class of Lévy-driven SDEs (2017, background): “1 with the gradient estimates in [27] we can easily prove the following statement which covers many interesting and important examples of Lévy processes, cf.”
- Harnack inequalities for stochastic equations driven by Levy noise (2012, background): “1(2) generalizes the main results in [16, 3, 12] for Lévy processes or linear equations driven by Lévy noise.”
- Gradient estimates of harmonic functions and transition densities for Levy processes (2013, background): “7 are of different form than those obtained in [28] and [16].”