Results 1 to 10 of about 2,001,462 (190)
A divergent, two-parameter, bounded martingale [PDF]
Proceedings of the American Mathematical Society, 1980 An example is given of a divergent, uniformly bounded martingale X = {
L. Dubins, J. Pitman
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Orlicz–Hardy Weak Martingale Spaces for Two-parameter
Taiwanese Journal of Mathematics, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kaituo Liu +3 more
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Stopping a two parameter weak martingale
Probability Theory and Related Fields, 1987 This paper deals with the following problem: Given a two parameter stochastic process, under what conditions is it possible to stop the process at any stopping line? It is shown that the class of stoppable processes is strictly larger than the class of two parameter integrators.
Ely Merzbach, M. Zakai
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r-variations for two-parameter continuous martingales and itô's formula
Stochastic Processes and their Applications, 1989 Let \(M=\{M_ z;z\in [0,1]^ 2\}\) be a two-parameter continuous martingale bounded in \(L^ 4\), and suppose that f is a real-valued function of class \(C^ 4\) such that \(f(0)=0\). The aim of this paper is to establish an Itô's formula of the type \[ f(M_ z)=\sum^{4}_{r=1}(r!)^{-1}\int_{[0,z]}f^{(r)}(M_ u)d\mu^ r_ M(u), \] where the processes \(\mu^ r_ ...
M. Sanz
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The continuity of the quadratic variation of two-parameter martingales
Stochastic Processes and their Applications, 1988 Let \(M=(M_ t;t\in {\mathbb{R}}^ 2_+)\) be an L \(log^+L\)-integrable two- parameter martingale. According to a theorem by \textit{D. Bakry} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 50, 149-157 (1979; Zbl 0419.60051)] and by \textit{A. Millet} and \textit{L. Sucheston} [ibid.
N. Frangos, P. Imkeller
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A property of two-parameter martingales with path-independent variation
Stochastic Processes and their Applications, 1987 The paper is devoted to some delicate and specific properties of two- parameter martingales. The authors consider continuous, vanishing on the axes, two-parameter martingales with path-independent variation (p.i.v.), i.e. their quadratic variations along all increasing paths from the origin and with the same end point have the same values.
D. Nualart, F. Utzet
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On the relations between increasing functions associated with two-parameter continuous martingales
Stochastic Processes and their Applications, 1990 Let \((\Omega,{\mathcal F},P,({\mathcal F}_ z)_{z\in T})\), \(T=[0,1]^ 2\), be a stochastic two-parameter basis satisfying the usual (F1)-(F4) conditions of Cairoli and Walsh. Let also M be a two-parameter continuous martingale bounded in \(L^ 2\) and null on the axes. Then \(M^ 2\) has the following Doob-Meyer decomposition: \[ M^ 2_{st}=2\int^{s}_{0}\
D. Nualart, M. Sanz, M. Zakai
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Littlewood–Paley–Rubio De Francia Inequality for the Two-Parameter Walsh System [PDF]
Journal of Mathematical Sciences, 2021 A version of Littlewood–Paley–Rubio de Francia inequality for the two-parameter Walsh system is proved: for any family of disjoint rectangles Ik=Ik1×Ik2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts ...
Viacheslav Borovitskiy
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Martingales and the fixation time of evolutionary graphs with arbitrary dimensionality
Royal Society Open Science, 2022 Evolutionary graph theory (EGT) investigates the Moran birth–death process constrained by graphs. Its two principal goals are to find the fixation probability and time for some initial population of mutants on the graph.
Travis Monk, André van Schaik
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Martingales and the characteristic functions of absorption time on bipartite graphs
Royal Society Open Science, 2021 Evolutionary graph theory investigates how spatial constraints affect processes that model evolutionary selection, e.g. the Moran process. Its principal goals are to find the fixation probability and the conditional distributions of fixation time, and ...
Travis Monk, André van Schaik
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