Husseini, Ryad: Jump processes with variable scaling parameters. - Bonn, 2010. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
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author = {{Ryad Husseini}},
title = {Jump processes with variable scaling parameters},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2010,
month = jan,

note = {The leitmotif of this thesis is non-locality. More precisely, it deals with a class of pure jump processes with space-dependent jump measures and with related non-local integrodifferential operators. Such objects arise in different contexts for example in partial differential equations. They have drawn increasing interest also by practioneers in the last years. This thesis wants to enlighten some important aspects of this theory. Each chapter contains results which are each of a different flavor.
Chapter 1 describes the general framework and surveys some results. Chapters 2 and 3 both study questions of regularity of solutions of non-local integro-differential operators - the first one by analytic means, i.e. pseudodifferential operator techniques, the second one by probabilistic means. Finally, chapter 4 studies Markov chain approximations of related jump processes. All chapters are self-contained. The results of Chapter 4 are published in [HK07] while the results of Chapter 2 and Chapter 3 are accepted for publication, see [AH08] and [HK09].},

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