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A growth estimate for continuous random fields

Ralf Manthey, Katrin Mittmann (1996)

Mathematica Bohemica

We prove a polynomial growth estimate for random fields satisfying the Kolmogorov continuity test. As an application we are able to estimate the growth of the solution to the Cauchy problem for a stochastic diffusion equation.

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

Let (Ω, , ( t )t≥0, ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to (theσ-algebra generated by ( t )t≥0) a coherent family of probability measures ( t ) indexed byt≥0, each of them being defined on 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, , ( t )t≥0, ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to (the σ-algebra generated by ( t )t≥0) a coherent family of probability measures ( t ) indexed by t≥0, each of them being defined on 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 remarkable σ -finite measure unifying supremum penalisations for a stable Lévy process

Yuko Yano (2013)

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

The σ -finite measure 𝒫 sup which unifies supremum penalisations for a stable Lévy process is introduced. Silverstein’s coinvariant and coharmonic functions for Lévy processes and Chaumont’s h -transform processes with respect to these functions are utilized for the construction of 𝒫 sup .

A uniform dimension result for two-dimensional fractional multiplicative processes

Xiong Jin (2014)

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

Given a two-dimensional fractional multiplicative process ( F t ) t [ 0 , 1 ] determined by two Hurst exponents H 1 and H 2 , we show that there is an associated uniform Hausdorff dimension result for the images of subsets of [ 0 , 1 ] by F if and only if H 1 = H 2 .

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