Victoria Knopova

A note on the existence of transition probability densities of Lévy processes

Abstract. We prove necessary and sufficient conditions for the existence of (smooth) transition probability densities for Lévy processes and isotropic Lévy processes. Under some mild conditions on the characteristic exponent we calculate the asymptotic behaviour of the transition density as and and show a ratio-limit theorem.

Parametrix construction of the transition probability density of the solution to an SDE driven by

Let

\alpha

L:= -a(x) (-\Delta)^{\alpha/2}+ (b(x), \nabla)

-stable noise

, where

Intrinsic small time estimates for distribution densities of Lévy processes

\alpha\in (0,2)

Parametrix construction for certain Lévy-type processes

, and

Accuracy of discrete approximation for integral functionals of Markov processes

a:\rd\to (0,\infty)

Stochastic Models of Financial Mathematics

,

A Probabilistic Proof of the Breakdown of Besov Regularity in L-Shaped Domains

b: \rd\to \rd

On the Feynman–Kac semigroup for some Markov processes

. Under certain regularity assumptions on the coefficients