Abstract
We consider random time changes in Markov processes with killing potentials. We study how random time changes may be introduced in these Markov processes with killing potential and how these changes may influence their time behavior. As applications, we study the parabolic Anderson problem, the non-local Schrödinger operators as well as the generalized Anderson problem.
Highlights
Let us underline that the random time change approach turns out to be a very effective tool in modeling several physical systems, spanning from ecological to biological, and in view of additional applications
The aim of this paper is to show how random time changes may be introduced in these Markov processes with killing potential and how these changes may influence their time behavior
We briefly describe the Anderson model in the framework of Markov processes with killing potential
Summary
Let us underline that the random time change approach turns out to be a very effective tool in modeling several physical systems, spanning from ecological to biological (see, for example, Magdziarz and Schilling [5] and the references therein), and in view of additional applications. All these considerations are related to the case of conservative Markov processes. The aim of this paper is to show how random time changes may be introduced in these Markov processes with killing potential and how these changes may influence their time behavior.
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