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Grobler, J. J.

Doob’s optional sampling theorem in Riesz spaces. (English) Zbl 1242.60041

Positivity 15, No. 4, 617-637 (2011).
This paper is a continuation of the author’s paper [Positivity 14, No. 4, 731–751 (2010; Zbl 1216.46005)] where the author defined continuous time stochastic processes in Riesz spaces and proved the Doob-Meyer decomposition theorem for martingales. In this paper the notions of stopping times and stopped processes for continuous stochastic processes are defined and studied in the framework of Riesz spaces. These considerations lead to a formulation and proof of Doob’s optimal sampling theorem.
Reviewer: Şafak Alpay (Ankara)

Cited in 16 Documents

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
46A40 Ordered topological linear spaces, vector lattices
60G44 Martingales with continuous parameter
60G07 General theory of stochastic processes

Keywords:

stochastic process with continuous parameter; vector lattice; stopping time; stopped process; conditional expectation; martingale

Citations:

Zbl 1216.46005
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Full Text: DOI

References:

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