Results 1 to 10 of about 94 (91)
Generalized kolmogorov inequalities for martingales [PDF]
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1976 The classical cebysev inequality leads to an inequality for martingales which is often called the Kolmogorov inequality. It is shown here that many generalized cebysev inequalities for random variables lead in a similar way to martingale inequalities, and that the corresponding martingale inequality is sharp when the cebysev inequality is.
Gilat, D., Sudderth, W. D.
openaire +2 more sources
A composite generalization of Ville's martingale theorem
CoRR, 2022 We provide a composite version of Ville's theorem that an event has zero measure if and only if there exists a nonnegative martingale which explodes to infinity when that event occurs. This is a classic result connecting measure-theoretic probability to the sequence-by-sequence game-theoretic probability, recently developed by Shafer and Vovk.
Johannes Ruf +3 more
openaire +2 more sources
Martingale Property of Generalized Stochastic Exponentials [PDF]
, 2012 For a real Borel measurable function b, which satisfies certain integrability conditions, it is possible to define a stochastic integral of the process b(Y) with respect to a Brownian motion W, where Y is a diffusion driven by W. It is well know that the stochastic exponential of this stochastic integral is a local martingale. In this paper we consider
Mijatovic, Aleksandar +2 more
openaire +2 more sources
Martingale representation in the enlargement of the filtration generated by a point process [PDF]
Stochastic Processes and their Applications, 2021 Let $X$ be a point process and let $\mathbb{X}$ denote the filtration generated by $X$. In this paper we study martingale representation theorems in the filtration $\mathbb{G}$ obtained as an initial and progressive enlargement of the filtration $\mathbb{X}$. The progressive enlargement is done here by means of a whole point process $H$.
Di Tella, Paolo, Jeanblanc, Monique
openaire +3 more sources
On the Martingale Property for Generalized Stochastic Processes [PDF]
Stochastics and Stochastic Reports, 1995 In the recent years, several groups have studied stochastic equations (e.g. SDE's, SPDE's, stochastic Volterra equations) outside the framework of the Ito calculus. Often, this led to solutions in spaces of generalized random processes or fields. It is therefore of interest to study the probabilistic properties of generalized stochastic processes, and ...
Benth, Fred Espen, Potthoff, Jürgen
openaire +3 more sources
Martingale Convergence of Generalized Conditional Expectations
Journal of Functional Analysis, 1993 A martingale convergence theorem for generalized conditional expectations is considered. It is, in its essence, a theorem on the convergence of the modular structures associated to a decreasing (increasing) sequence of von Neumann algebras, to the corresponding modular structures associated to the intersection (closure of the union) of the given ...
ACCARDI, LUIGI, LONGO, ROBERTO
openaire +3 more sources
A Generalized Martingale Betting Strategy
Missouri Journal of Mathematical Sciences, 2009 A generalized martingale betting strategy is analyzed for which bets are increased by a factor of $m \geq 1$ after each loss, but return to the initial bet amount after each win. The average amount bet and the average final fortune are derived for sequences of $n$ bets, for the number of bets $T$ that results in the first win, and for $\min (T,\;n)$.
Neal, David K., Russell, Michael D.
openaire +2 more sources
A martingale approach to general Franklin systems [PDF]
Studia Mathematica, 2006 We prove unconditionality of general Franklin systems in Lp(X), where X is a UMD space and where the general Franklin system corresponds to a quasi-dyadic, weakly regular sequence of knots.
Anna Kamont, Paul F. X. Müller
openaire +1 more source
Synonymity, Generalized Martingales, and Subfiltration
The Annals of Probability, 1984 The notion of synonymity of two processes X and Y refines the notion of ''X and Y having the same law'' by taking into account the relation of the processes to their underlying filtrations. Synonymity was introduced by \textit{D. J. Aldous} [Ecole d'Été de Saint-Flour 1983, to appear in Lect.
openaire +3 more sources
Cylindrical Martingale Problems Associated with Lévy Generators [PDF]
Journal of Theoretical Probability, 2018 We introduce and discuss Lévy-type cylindrical martingale problems on separable reflexive Banach spaces. Our main observations are the following: Cylindrical martingale problems have a one-to-one relation to weak solutions of stochastic partial differential equations. Moreover, well-posed problems possess the strong Markov property and a Cameron-Martin-
openaire +2 more sources