Estimates of transition densities and their derivatives for jump Lévy processes

By K. Kaleta, Paweł Sztonyk. 2013

70 citations recorded by the source corpus.

Abstract We give upper and lower estimates of densities of convolution semigroups of probability measures under explicit assumptions on the corresponding Levy measure and the Levy–Khinchin exponent. We obtain also estimates of derivatives of densities.

Subfields: Finance, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1cde5416d35f5c4b134894bedd586eede3817734

How researchers see this paper

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

In Finance

1. Tadeusz Kulczycki
2. M. Ryznar
3. Ante Mimica
4. Renming Song
5. Krzysztof Bogdan
6. Mateusz Kwaśnicki
7. Bartłlomiej Dyda
8. T. Grzywny

In Management Science and Operations Research

1. M. Ryznar
2. Tadeusz Kulczycki
3. Ante Mimica

In Mathematical Physics

1. Tadeusz Kulczycki
2. Ante Mimica
3. M. Ryznar
4. Renming Song
5. Bartłlomiej Dyda
6. Mateusz Kwaśnicki
7. Krzysztof Bogdan
8. Zhen-Qing Chen

Citations in the corpus

• Heat kernel estimates for subordinate Brownian motions (2015, methodology): “Some far from optimal upper bounds in this case were obtained earlier in [15, 21].”
• Gradient estimates of harmonic functions and transition densities for Levy processes (2013, result): “stimates of the corresponding transition semigroups were derived. They are of the type ||∇Ptu||∞ ≤ c||u||∞f−1(1/t), u∈ Bb(Rd), where |ℜψ(ξ)| ≈ f(|ξ|) as |ξ| → ∞. Recently, K. Kaleta and P. Sztonyk in [16] obtained also gradient estimates of transition densities for L´evy processes. Note that our sha”