Transition Density Estimates for a Class of Lévy and Lévy-Type Processes

By Viktorya Knopova, René L. Schilling. 2009

49 citations recorded by the source corpus.

We show on- and off-diagonal upper estimates for the transition densities of symmetric Lévy and Lévy-type processes. To get the on-diagonal estimates, we prove a Nash-type inequality for the related Dirichlet form. For the off-diagonal estimates, we assume that the characteristic function of a Lévy(-type) process is analytic, which allows us to apply the complex analysis technique.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f7815eae9fc8951bf1e8f4d3c9bedfd3c9ed5776

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In Applied Mathematics

In Finance

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Citations in the corpus

Density and tails of unimodal convolution semigroups (2013, methodology): “We remark that analogues of the on-diagonal term [ψ−(1/t)]d ≈ pt(0) in (2) are often obtained for more general Markov processes via Nash and Sobolev inequalities [3, 8, 2, 29, 21].”
Heat kernel estimates for subordinate Brownian motions (2015, unknown): “This type of estimate can be found in [20] for more general Lévy processes via Nash inequality.”
Gradient estimate for Ornstein–Uhlenbeck jump processes (2010, methodology): “rocess is pure jump, existence and regularities of the transition density have been derived by using conditions on the symbol ∗Supported in part by WIMCS, NNSFC(10721091). 1 or the L´evy measure (see [8, 9, 12] and references within); see also [5, 11] for heat kernel upper bounds for α-stable proces”