Transportation distance between the Lévy measures and stochastic equations for Lévy-type processes
Volume 1, Issue 1 (2014), pp. 49–64
Pub. online: 27 June 2014
Type: Research Article
Open Access
Open Access
Received
10 April 2014
10 April 2014
Revised
2 June 2014
2 June 2014
Accepted
5 June 2014
5 June 2014
Published
27 June 2014
27 June 2014
Abstract
The notion of the transportation distance on the set of the Lévy measures on $\mathbb{R}$ is introduced. A Lévy-type process with a given symbol (state dependent analogue of the characteristic triplet) is proved to be well defined as a strong solution to a stochastic differential equation (SDE) under the assumption of Lipschitz continuity of the Lévy kernel in the symbol w.r.t. the state space variable in the transportation distance. As examples, we construct Gamma-type process and α-stable like process as strong solutions to SDEs.
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