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Stopped processes and Doob's optional sampling theorem [PDF]
Journal of Mathematical Analysis and Applications, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jacobus J Grobler
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The Optional Sampling Theorem for Martingales Indexed by Directed Sets
Annals of Probability, 1980 A natural generalization of the optional sampling theorem for martingales is given. For discrete valued stopping times the result holds for directed sets; for more general stopping times the result holds for lattices satisfying a type of separability condition. The discrete case improves a lemma of Chow.
Thomas G Kurtz
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The optional sampling theorem for submartingales in the sequentially planned context
Statistics and Probability Letters, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fenoy, M. Mar, Ibarrola, Pilar
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The Optional Sampling Theorem for Processes Indexed by a Partially Ordered Set
Annals of Probability, 1985 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Doob’s optional sampling theorem in Riesz spaces
Positivity, 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 ...
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A CENTRAL LIMIT THEOREM FOR LATIN HYPERCUBE SAMPLING WITH DEPENDENCE AND APPLICATION TO EXOTIC BASKET OPTION PRICING [PDF]
International Journal of Theoretical and Applied Finance, 2012 We consider the problem of estimating 𝔼[f(U1, …, Ud)], where (U1, …, Ud) denotes a random vector with uniformly distributed marginals. In general, Latin hypercube sampling (LHS) is a powerful tool for solving this kind of high-dimensional numerical integration problem. In the case of dependent components of the random vector (U1, …, Ud) one can achieve
CHRISTOPH AISTLEITNER +2 more
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Stopped processes and Doob's optional sampling theorem
, 2020 Using the spectral measure $μ_\mathbb{S}$ of the stopping time $\mathbb{S},$ we define the stopping element $X_\mathbb{S}$ as a Daniell integral $\int X_t\,dμ_\mathbb{S}$ for an adapted stochastic process $(X_t)_{t\in J}$ that is a Daniell summable vector-valued function.
Grobler, Jacobus J. +1 more
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Beyond Wald's Equation and the Optional Sampling Theorem
This paper establishes a conservation identity for mean-zero martingales stopped by extended-valued stopping times. For any mean-zero martingale $\{M_n\}$ and any extended-valued stopping time $T$ satisfying $E|M_T|I(T<\infty)<\infty$, the quantity $L\equiv E[M_T I(T<\infty)]$ exists and equals $\lim_n E[-M_n I(T>n)]$, a limit which always ...
Klass, Michael, de la Pena, Victor
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This paper extends classical probabilistic results to the broader class of demimartingales and demisubmartingales. We establish variants of Doob's-type optional sampling theorem under minimal structural conditions on stopping times, relying on monotonicity properties of indicator functions.
Hadjikyriakou, Milto +1 more
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