Search results for "Martingales"

showing 4 items of 4 documents

Le martingale: aspetti teorici ed applicativi

2001

This paper offers an overview on the characteristics of martingales. These latter are markovian processes without underlying trend, in which the stochastic variable depends on its ultimate realisation. Some application fields are in studies relative to financial markets, and especially the derivative securities. Drawing from the theoretical and empirical literature, the main mathematical characteristics are presented. In order to transform processes with increasing or decreasing trends into martingales, the Doob-Meyer decomposition and the change of probability measure approaches can be adopted. Finally, four applications are considered with regard to the pricing of futures, call options an…

Martingales stochastic processes calculus of probabilitySettore MAT/06 - Probabilita' E Statistica Matematica
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On decoupling in Banach spaces

2021

AbstractWe consider decoupling inequalities for random variables taking values in a Banach space X. We restrict the class of distributions that appear as conditional distributions while decoupling and show that each adapted process can be approximated by a Haar-type expansion in which only the pre-specified conditional distributions appear. Moreover, we show that in our framework a progressive enlargement of the underlying filtration does not affect the decoupling properties (in particular, it does not affect the constants involved). As a special case, we deal with one-sided moment inequalities for decoupled dyadic (i.e., Paley–Walsh) martingales and show that Burkholder–Davis–Gundy-type in…

Statistics and ProbabilityPure mathematicsGeneral MathematicsBanach space01 natural sciences010104 statistics & probabilityFOS: MathematicsFiltration (mathematics)decoupling in Banach spaces0101 mathematicsSpecial casestokastiset prosessitMathematicsMathematics::Functional Analysisdyadic martingalesProbability (math.PR)010102 general mathematicsDecoupling (cosmology)Conditional probability distributionBanachin avaruudetAdapted processMoment (mathematics)regular conditional probabilities60E15 60H05 46B09stochastic integrationStatistics Probability and UncertaintyfunktionaalianalyysiRandom variableMathematics - Probability
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Recursion at the crossroads of sequence modeling, random trees, stochastic algorithms and martingales

2013

This monograph synthesizes several studies spanning from dynamical systems in the statistical analysis of sequences, to analysis of algorithms in random trees and discrete stochastic processes. These works find applications in various fields ranging from biological sequences to linear regression models, branching processes, through functional statistics and estimates of risk indicators for insurances. All the established results use, in one way or another, the recursive property of the structure under study, by highlighting invariants such as martingales, which are at the heart of this monograph, as tools as well as objects of study.

modèles auto-régressifs[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]estimation and prediction errorstochastic gradient algorithmschaîne de Markov à mémoire variable[STAT.TH] Statistics [stat]/Statistics Theory [stat.TH]Digital search treesvariable length Markov chainstrong laws for discrete martingalessuffix trietemps d'occurrences de motifsoptimisation stochastique.dynamical systemtrie des suffixesstochastic optimization.erreur d'estimation et de prédictionArbres digitaux de rechercheauto-regressive modelssystème dynamiquelois fortes de martingales discrètesalgorithmes de gradient stochastiques[MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]occurrences time
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MR2407444 (2009e:60101) Labuschagne, Coenraad C. A. Join-semilattices of integrable set-valued martingales. Thai J. Math. 5 (2007), no. 1, 53--69. (R…

2009

Join-semilattices of integrable set-valued martingales

set-valued martingales
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