Results 1 to 10 of about 314 (125)
On the Quadratic Variation of Two-Parameter Continuous Martingales
Annals of Probability, 1984 Let M={M(z),z∈[0,1]2} be a two-parameter square integrable continuous martingale. We prove the sample continuity of the quadratic variation of M using an Ito's differentiation formula for M2.
D Nualart
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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_ ...
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A stochastic calculus for continuous N-parameter strong martingales
Stochastic Processes and Their Applications, 1985 Let M be a 4N-integrable, real-valued continuous N-parameter strong martingale with respect to an increasing family of \(\sigma\)-fields satisfying the conditional independence property introduced by \textit{R. Cairoli} and \textit{J. B. Walsh}, Acta Math. 134, 111-183 (1975; Zbl 0334.60026).
Peter Imkeller
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Local Time for Two-Parameter Continuous Martingales with Respect to the Quadratic Variation
Annals of Probability, 1988 The author studies the local time for two-parameter continuous martingales M as a density of the ``measure of sojourn time'' with respect to the quadratic variation \(\). First she shows that there exists a process \(\{L(x,s,t);\) \(x\in {\mathbb{R}}\setminus \{0\},\) \((s,t)\in {\mathbb{R}}^ 2_+\}\) satisfying the occupation density formula and which ...
exaly +4 more sources
A stochastic card balance management problem with continuous and batch-type bilateral transactions
Operations Research Perspectives, 2023 We study a stochastic continuous-review card balance management problem with two transaction patterns, namely, continuous and batch-type bilateral transactions, both in a Markovian environment.
Yonit Barron
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On representation and regularity of continuous parameter multivalued martingales [PDF]
Proceedings of the American Mathematical Society, 1998 In this paper we study multivalued martingales in continuous time. First we show that every multivalued martingale in continuous time can be represented as the closure of a sequence of martingale selections. Then we prove two results concerning the cadlag modifications of continuous time multivalued martingales, in Kuratowski-Mosco convergence and in ...
Dong, Wenlong, Wang, Zhenpeng
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Continuous-Parameter Martingales
Journal of Multivariate Analysis, 2002 The second part of this book starts with a continuous-parameter extension of the discrete-parameter theory of Chapter 1. Our use of the term “extension” is quite misleading. Indeed, we will quickly find that in order to carry out these “extensions,” one needs a good understanding of the regularity of the sample functions of multiparameter stochastic ...
Edgar, Gerald A, Sucheston, Louis
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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.
Frangos, Nikos E., Imkeller, Peter
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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}\
Nualart, D., Sanz, M., Zakai, M.
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Local times of continuous N-parameter strong martingales
Journal of Multivariate Analysis, 1986 This paper studies the properties of local times of continuous N- parameter strong martingales. Suppose that \(M=\{M(z)\), \(z\in [0,1]^ N\}\) is a 4N-integrable, real-valued continuous N-parameter strong martingale with respect to a family of \(\sigma\)-fields \(\{\) \({\mathcal F}_ z\), \(z\in [0,1]^ N\}\) verifying the usual conditional independence
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