Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Levi’s parametrix method

Sortuj według:

Ogranicz wyniki do:

Regularity of fundamental solutions for Lévy-type operators

Szczypkowski Karol

Bulletin of the Polish Academy of Sciences. Mathematics

2023

Vol. 71, no 2

169--191

For a class of non-symmetric non-local Lévy-type operators Lκ, which include those of the form Lκf(x) := Rd(f(x + z) − f(x) − 1|z|<1⟨z, ∇f(x)⟩)κ(x, z)J(z) dz, e prove regularity of the fundamental solution pκ to the equation ∂t = Lκ.

Intrinsic compound kernel estimates for the transition probability density of Lévy-type processes and their applications

Knopova V., Kulik A.

Probability and Mathematical Statistics

2017

Vol. 37, Fasc. 1

53--100

Starting with an integro-differential operator (L, C2∞ (Rn)), we prove that its C∞(Rn)-closure is the generator of a Feller process X, which admits a transition probability density. To construct this transition probability density, we develop a version of the parametrix method and a verification procedure, which proves that the constructed object is the claimed one. As a part of the construction, we prove the intrinsic upper and lower estimates on the density. As an application of the constructed estimates we state the necessary and (separately) sufficient conditions under which a given Borel measure belongs to the Kato and Dynkin classes with respect to the constructed transition probability density.