Abstract
Classically, a Lévy process is defined as a stochastically continuous process, pinned to the origin, with independent and stationary increments (cf. e.g. Sato [71]). Lévy processes have also been studied by the means of Robinsonian nonstandard analysis (in particular by Lindstrøm [49] with sequels by Albeverio and Herzberg [2], Lindstrøm [50], Albeverio et al. [1, Chap. 5], Herzberg and Lindstrøm [36] and [33]).
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Notes
- 1.
In the classical setting, these processes correspond to Lévy walks whose Lévy measure is concentrated on a set that is bounded from below in norm.
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Herzberg, F.S. (2013). A Radically Elementary Theory of Lévy Processes. In: Stochastic Calculus with Infinitesimals. Lecture Notes in Mathematics, vol 2067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33149-7_9
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