Relevant bibliographies by topics / Martingale Sequence

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Martingale Sequence'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Martingale Sequence"

1

Jones, Martin L. "A note on dilations and martingales." International Journal of Mathematics and Mathematical Sciences 16, no. 4 (1993): 825–27. http://dx.doi.org/10.1155/s016117129300105x.

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The purpose of this note is to investigate the effect of dilations on martingales and to give conditions under which a dilated martingale will retain the martingale property. The technique of dilating the joint distribution of a sequence of random variables has applications in optimal stopping theory and the study of “prophet inequalities” where martingales play a significant role.
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PARCET, JAVIER, and NARCISSE RANDRIANANTOANINA. "GUNDY'S DECOMPOSITION FOR NON-COMMUTATIVE MARTINGALES AND APPLICATIONS." Proceedings of the London Mathematical Society 93, no. 1 (2006): 227–52. http://dx.doi.org/10.1017/s0024611506015863.

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We provide an analogue of Gundy's decomposition for $L_1$-bounded non-commutative martingales. An important difference from the classical case is that for any $L_1$-bounded non-commutative martingale, the decomposition consists of four martingales. This is strongly related with the row/column nature of non-commutative Hardy spaces of martingales. As applications, we obtain simpler proofs of the weak type $(1,1)$ boundedness for non-commutative martingale transforms and the non-commutative analogue of Burkholder's weak type inequality for square functions. A sequence $(x_n)_{n \ge 1}$ in a norm
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EL MACHKOURI, MOHAMED, and DALIBOR VOLNÝ. "ON THE CENTRAL AND LOCAL LIMIT THEOREM FOR MARTINGALE DIFFERENCE SEQUENCES." Stochastics and Dynamics 04, no. 02 (2004): 153–73. http://dx.doi.org/10.1142/s021949370400105x.

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Let [Formula: see text] be a Lebesgue space and T: Ω→Ω an ergodic measure-preserving automorphism with positive entropy. We show that there is a bounded and strictly stationary martingale difference sequence defined on Ω with a common nondegenerate lattice distribution satisfying the central limit theorem with an arbitrarily slow rate of convergence and not satisfying the local limit theorem. A similar result is established for martingale difference sequences with densities provided the entropy is infinite. In addition, the martingale difference sequence may be chosen to be strongly mixing.
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Dai, Hongshuai, Tien-Chung Hu, and June-Yung Lee. "Operator Fractional Brownian Motion and Martingale Differences." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/791537.

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It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both applications and theory. In this paper, we study the relation between them. We construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence.
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Wang, Xuejun, Shuhe Hu, Wenzhi Yang, and Xinghui Wang. "Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences." Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/572493.

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We study the complete convergence and complete moment convergence for martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As a result, the Marcinkiewicz-Zygmund strong law of large numbers for martingale difference sequence is obtained. Our results generalize the corresponding ones of Stoica (2007, 2011).
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Phillips, P. C. B. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals Via Martingale Approximations." Econometric Theory 4, no. 3 (1988): 528–33. http://dx.doi.org/10.1017/s026646660001344x.

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Under general conditions the sample covariance matrix of a vector martingale and its differences converges weakly to the matrix stochastic integral ∫01BdB′, where B is vector Brownian motion. For strictly stationary and ergodic sequences, rather than martingale differences, a similar result obtains. In this case, the limit is ∫01BdB′ + Λ and involves a constant matrix Λ of bias terms whose magnitude depends on the serial correlation properties of the sequence. This note gives a simple proof of the result using martingale approximations.
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Jena, Bidu Bhusan, and Susanta Kumar Paikray. "A certain class of statistical convergence of martingale sequences and its applications to Korovkin-type approximation." Annals of the University of Craiova, Mathematics and Computer Science Series 49, no. 1 (2022): 146–57. http://dx.doi.org/10.52846/ami.v49i1.1523.

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In this paper, we investigate and study the notions of statistical product convergence and statistical product summability via deferred Cesàro and deferred Nörlund product means for martingale sequences of random variables. We then establish an inclusion theorem concerning the relation between these two beautiful and definitively useful concepts. Also, based upon our proposed ideas, we demonstrate new thoughtful approximation of Korovkin-type theorems for a martingale sequence over a Banach space. Moreover, we establish that our theorems effectively extend and improve most (if not all) of the
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Lynch, James D. "The Galton-Watson process revisited: some martingale relationships and applications." Journal of Applied Probability 37, no. 02 (2000): 322–28. http://dx.doi.org/10.1017/s0021900200015540.

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A martingale is used to study extinction probabilities of the Galton-Watson process using a stopping time argument. This same martingale defines a martingale function in its arguments; consequently, its derivative is also a martingale. The argumentscan be classified as regular or irregular and this classification dictates very different behavior of the Galton-Watson process. For example, it is shown that irregularity of a pointsis equivalent to the derivative martingale sequence atsbeing closable, (i.e., it has limit which, when attached to the original sequence, the martingale structure is re
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Yurachkivsky, Andriy. "Convergence of Locally Square Integrable Martingales to a Continuous Local Martingale." Journal of Probability and Statistics 2011 (2011): 1–34. http://dx.doi.org/10.1155/2011/580292.

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Let for each be an -valued locally square integrable martingale w.r.t. a filtration (probability spaces may be different for different ). It is assumed that the discontinuities of are in a sense asymptotically small as and the relation holds for all , row vectors , and bounded uniformly continuous functions . Under these two principal assumptions and a number of technical ones, it is proved that the 's are asymptotically conditionally Gaussian processes with conditionally independent increments. If, moreover, the compound processes converge in distribution to some , then a sequence () converge
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Lynch, James D. "The Galton-Watson process revisited: some martingale relationships and applications." Journal of Applied Probability 37, no. 2 (2000): 322–28. http://dx.doi.org/10.1239/jap/1014842539.

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A martingale is used to study extinction probabilities of the Galton-Watson process using a stopping time argument. This same martingale defines a martingale function in its argument s; consequently, its derivative is also a martingale. The argument s can be classified as regular or irregular and this classification dictates very different behavior of the Galton-Watson process. For example, it is shown that irregularity of a point s is equivalent to the derivative martingale sequence at s being closable, (i.e., it has limit which, when attached to the original sequence, the martingale structur
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Dissertations / Theses on the topic "Martingale Sequence"

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Delbaen, Freddy, and Walter Schachermayer. "A compactness principle for bounded sequences of martingales with applications." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/1604/1/document.pdf.

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For H^1 bounded sequences, we introduce a technique, related to the Kadec-Pelczynski -decomposition for L^1 sequences, that allows us to prove compactness theorems. Roughly speaking, a bounded sequence in H^1 can be split into two sequences, one of which is weakly compact, the other forms the singular part. If the martingales are continuous then the singular part tends to zero in the semi-martingale topology. In the general case the singular parts give rise to a process of bounded variation. The technique allows to give a new proof of the optional decomposition theorem in Mathematical Finance.
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Paditz, Ludwig. "Beiträge zur expliziten Fehlerabschätzung im zentralen Grenzwertsatz." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-115105.

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In der Arbeit wird das asymptotische Verhalten von geeignet normierten und zentrierten Summen von Zufallsgrößen untersucht, die entweder unabhängig sind oder im Falle der Abhängigkeit als Martingaldifferenzfolge oder stark multiplikatives System auftreten. Neben der klassischen Summationstheorie werden die Limitierungsverfahren mit einer unendlichen Summationsmatrix oder einer angepaßten Folge von Gewichtsfunktionen betrachtet. Es werden die Methode der charakteristischen Funktionen und besonders die direkte Methode der konjugierten Verteilungsfunktionen weiterentwickelt, um quantitative Aussa
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"A compactness principle for bounded sequences of martingales with applications." SFB Adaptive Information Systems and Modelling in Economics and Management Science, 1999. http://epub.wu-wien.ac.at/dyn/dl/wp/epub-wu-01_1cc.

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MINOZZO, Marco. "On some aspects of the prequential and algorithmic approaches to probability and statistical theory." Doctoral thesis, 1996. http://hdl.handle.net/11562/385444.

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La tesi di dottorato prende spunto dallo studio di un nuovo approccio all’inferenza statistica, chiamato “prequential approach”, proposto da A. Philip Dawid. Nel caso di un insieme di osservazioni ottenute in modo sequenziale, in cui ogni nuova osservazione è preceduta da una previsione probabilistica circa il suo possibile valore, fatta sulla base delle osservazioni passate e di un qualche modello, questo approccio richiede che la valutazione empirica di tale modello dipenda solo dalla sequenza delle previsioni effettivamente fatte. Seguendo lo sviluppo di alcune idee emerse da questo approc
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Paditz, Ludwig. "Beiträge zur expliziten Fehlerabschätzung im zentralen Grenzwertsatz." Doctoral thesis, 1988. https://tud.qucosa.de/id/qucosa%3A26930.

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In der Arbeit wird das asymptotische Verhalten von geeignet normierten und zentrierten Summen von Zufallsgrößen untersucht, die entweder unabhängig sind oder im Falle der Abhängigkeit als Martingaldifferenzfolge oder stark multiplikatives System auftreten. Neben der klassischen Summationstheorie werden die Limitierungsverfahren mit einer unendlichen Summationsmatrix oder einer angepaßten Folge von Gewichtsfunktionen betrachtet. Es werden die Methode der charakteristischen Funktionen und besonders die direkte Methode der konjugierten Verteilungsfunktionen weiterentwickelt, um quantitative Aussa
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Books on the topic "Martingale Sequence"

1

Merlevède, Florence, Magda Peligrad, and Sergey Utev. Functional Gaussian Approximation for Dependent Structures. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198826941.001.0001.

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This book has its origin in the need for developing and analyzing mathematical models for phenomena that evolve in time and influence each another, and aims at a better understanding of the structure and asymptotic behavior of stochastic processes. This monograph has double scope. First, to present tools for dealing with dependent structures directed toward obtaining normal approximations. Second, to apply the normal approximations presented in the book to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including
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Book chapters on the topic "Martingale Sequence"

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Astashkin, Sergey V. "Martingale Transforms of the Rademacher Sequence in Symmetric Spaces." In The Rademacher System in Function Spaces. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47890-2_13.

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Shiryaev, Albert N. "Martingale Sequences." In Problem Books in Mathematics. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3688-1_7.

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Zinn, Joel. "Comparison of martingale difference sequences." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074966.

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Shiryaev, A. N. "Sequences of Random Variables That Form Martingales." In Graduate Texts in Mathematics. Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4757-2539-1_8.

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Metivier, Michel. "Tightness Of Sequences Of Hilbert Valued Martingales." In Stochastic Space—Time Models and Limit Theorems. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5390-1_11.

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Delbaen, F., and W. Schachermayer. "A Compactness Principle for Bounded Sequences of Martingales with Applications." In Seminar on Stochastic Analysis, Random Fields and Applications. Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8681-9_10.

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Baker, David, Catherine Donati-Martin, and Marc Yor. "A Sequence of Albin Type Continuous Martingales with Brownian Marginals and Scaling." In Séminaire de Probabilités XLIII. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15217-7_20.

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Davis, Burgess, and Renming Song. "A Geometrical Characterization of Banach Spaces in Which Martingale Difference Sequences are Unconditional." In Selected Works of Donald L. Burkholder. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-7245-3_23.

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Rosiński, Jan. "Strong Exponential Integrability of Martingales with Increments Bounded by a Sequence of Numbers." In High Dimensional Probability II. Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1358-1_5.

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Grimmett, Geoffrey R., and David R. Stirzaker. "Convergence of random variables." In Probability and Random Processes. Oxford University PressOxford, 2001. http://dx.doi.org/10.1093/oso/9780198572237.003.0007.

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Abstract The many modes of convergence of a sequence of random variables are discussed and placed in context, and criteria are developed for proving convergence. These include standard inequalities, Skorokhod’s theorem, the Borel–Cantelli lemmas, and the zero–one law. Laws of large numbers, including the strong law, are proved using elementary arguments. Martingales are defined, and the martingale convergence theorem proved, with applications. The relationship between prediction and conditional expectation is explored, and the condition of uniform integrability described.
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