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On a Lévy process pinned at random time

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Abstract In this paper, our first goal is to rigorously define a Lévy process pinned at random time. Our second task is to establish the Markov property with respect to… Click to show full abstract

Abstract In this paper, our first goal is to rigorously define a Lévy process pinned at random time. Our second task is to establish the Markov property with respect to its completed natural filtration and thus with respect to the usual augmentation of the latter. The resulting conclusion is the right-continuity of completed natural filtration. Certain examples of such process are considered.

Keywords: pinned random; process pinned; process; random time

Journal Title: Forum Mathematicum
Year Published: 2020

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