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A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

Let (Ω, ℱ , ( ℱ t )t≥0, ℙ ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to ℱ ∞ (theσ-algebra generated by ( ℱ t )t≥0) a coherent family of probability measures ( ℚ t ) indexed byt≥0, each of them being defined on ℱ t . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual augmentation....

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

Let (Ω, ℱ , ( ℱ t )t≥0, ℙ ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to ℱ ∞ (the σ-algebra generated by ( ℱ t )t≥0) a coherent family of probability measures ( ℚ t ) indexed by t≥0, each of them being defined on ℱ t . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual...

A new proof of Kellerer’s theorem

Francis Hirsch, Bernard Roynette (2012)

ESAIM: Probability and Statistics

In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.

A new proof of Kellerer’s theorem

Francis Hirsch, Bernard Roynette (2012)

ESAIM: Probability and Statistics

In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.

A new weighted Gompertz distribution with applications to reliability data

Hassan S. Bakouch, Ahmed M. T. Abd El-Bar (2017)

Applications of Mathematics

A new weighted version of the Gompertz distribution is introduced. It is noted that the model represents a mixture of classical Gompertz and second upper record value of Gompertz densities, and using a certain transformation it gives a new version of the two-parameter Lindley distribution. The model can be also regarded as a dual member of the log-Lindley- X family. Various properties of the model are obtained, including hazard rate function, moments, moment generating function, quantile function,...

A noise of new type and its generalized functionals

Takeyuki Hida (2011)

Banach Center Publications

The purpose of this paper is to introduce a new noise denoted by P'(u). It has the space parameter u, being compared with the usual noise depending on the time t. We first explain why such a noise arises naturally. Then, we come to the analysis of functionals of this new noise. We shall emphasize the significance of generalized functionals of P'(u), in particular, linear and quadratic.

A nonasymptotic theorem for unnormalized Feynman–Kac particle models

F. Cérou, P. Del Moral, A. Guyader (2011)

Annales de l'I.H.P. Probabilités et statistiques

We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first...

Currently displaying 341 – 360 of 1378