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Witold Bednorz (2012)
Bulletin of the Polish Academy of Sciences. Mathematics
Talagrand's proof of the sufficiency of existence of a majorizing measure for the sample boundedness of processes with bounded increments used a contraction from a certain ultrametric space. We give a short proof of existence of such an ultrametric using admissible sequences of nets.
Russell Lyons, Yuval Peres, Oded Schramm (2003)
Annales de l'I.H.P. Probabilités et statistiques
Richard F. Bass (1984)
Séminaire de probabilités de Strasbourg
Bulatovic, Jelena (1981)
Publications de l'Institut Mathématique. Nouvelle Série
Claire Dupuis (1974)
Séminaire de probabilités de Strasbourg
Vadym Radchenko (2009)
Studia Mathematica
The stochastic heat equation on [0,T]×ℝ driven by a general stochastic measure is investigated. Existence and uniqueness of the solution is established. Hölder regularity of the solution in time and space variables is proved.
Peter Eichelsbacher (2001)
Annales de l'I.H.P. Probabilités et statistiques
P. Boulicaut (1974)
Annales scientifiques de l'Université de Clermont. Mathématiques
R. A. Doney, R. A. Maller (2004)
Annales de l'I.H.P. Probabilités et statistiques
Adriano Garsia, Eugène Rodemich (1974)
Annales de l'institut Fourier
We show here that a wide class of integral inequalities concerning functions on can be obtained by purely combinatorial methods. More precisely, we obtain modulus of continuity or other high order norm estimates for functions satisfying conditions of the type where and are monotone increasing functions of .Several applications are also derived. In particular these methods are shown to yield a new condition for path continuity of general stochastic processes
Barral, Julien, Lévy Véhel, Jacques (2004)
Electronic Journal of Probability [electronic only]
Mannersalo, Petteri, Norros, Ilkka, Riedi, Rudolf H. (2010)
Journal of Probability and Statistics
Dmitry Dolgopyat, Vadim Sidorov (1995)
Fundamenta Mathematicae
We study Brownian zeroes in the neighborhood of which one can observe a non-typical growth rate of Brownian excursions. We interpret the multifractal curve for the Brownian zeroes calculated in [6] as the Hausdorff dimension of certain sets. This provides an example of the multifractal analysis of a statistically self-similar random fractal when both the spacing and the size of the corresponding nested sets are random.
Antoine Ayache, Murad S. Taqqu (2005)
Publicacions Matemàtiques
Multifractional Processes with Random Exponent (MPRE) are obtained by replacing the Hurst parameter of Fractional Brownian Motion (FBM) with a stochastic process. This process need not be independent of the white noise generating the FBM. MPREs can be conveniently represented as random wavelet series. We will use this type of representation to study their Hölder regularity and their self-similarity.
Antoine Ayache, Narn-Rueih Shieh, Yimin Xiao (2011)
Annales de l'I.H.P. Probabilités et statistiques
By using a wavelet method we prove that the harmonisable-type N-parameter multifractional brownian motion (mfBm) is a locally nondeterministic gaussian random field. This nice property then allows us to establish joint continuity of the local times of an (N, d)-mfBm and to obtain some new results concerning its sample path behavior.
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