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Lévy processes in the physical sciences. (English) Zbl 0982.60043
Barndorff-Nielsen, Ole E. (ed.) et al., Lévy processes. Theory and applications. Boston: Birkhäuser. 241-266 (2001).
An \(\mathbb R^d\)-valued stochastic process \((X(t))_{t\geq 0}\) is said to be a Levy process provided it has time homogeneous and independent increments. A detailed investigation of those processes may be found in the book of J. Bertoin [“Lévy processes” (1996; Zbl 0861.60003)]. Among Lévy processes the class of stable ones is of special interest and importance. Recall that they enjoy certain self-similarity properties. The aim of the present paper is to review a number of physical phenomena for which Lévy processes and, in particular, stable processes can be used as a reasonable model. The examples are from fluid mechanics, solid state physics, polymer chemistry and mathematical finance. For certain nonlinear problems, asymptotic and approximation schemes are discussed.
For the entire collection see [Zbl 0961.00012].

MSC:
60G51 Processes with independent increments; Lévy processes
60K40 Other physical applications of random processes
60G52 Stable stochastic processes
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