A critical function for the planar brownian convex hull
A formula for densities of transition functions
A growth estimate for continuous random fields
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
Let (Ω, , ()t≥0, ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to (theσ-algebra generated by ()t≥0) a coherent family of probability measures () indexed byt≥0, each of them being defined on . 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
Let (Ω, , ()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≥0) a coherent family of probability measures () indexed by t≥0, each of them being defined on . 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 non-Markovian process with unbounded -variation.
A non-Skorokhod topology on the Skorokhod space.
A note on local asymptotic behavior for Brownian motion in Banach spaces.
A probabilistic approach to the asymptotics of the length of the longest alternating subsequence.
A proof from `first principles' of Kesten's result for the probabilities with which a subordinator hits points.
A remark on the r-th mean differentiability.
A remarkable -finite measure unifying supremum penalisations for a stable Lévy process
The -finite measure which unifies supremum penalisations for a stable Lévy process is introduced. Silverstein’s coinvariant and coharmonic functions for Lévy processes and Chaumont’s -transform processes with respect to these functions are utilized for the construction of .
A short proof of the Hausdorff dimension formula for Lévy processes.
A simple proof of the support theorem for diffusion processes
A uniform dimension result for two-dimensional fractional multiplicative processes
Given a two-dimensional fractional multiplicative process determined by two Hurst exponents and , we show that there is an associated uniform Hausdorff dimension result for the images of subsets of by if and only if .
Absolute continuity of Markov processes
Almost-sure path properties of fractional brownian sheet
Amplitude du mouvement Brownien et juxtaposition des excursions positives et négatives
An asymptotic bound for the tail of the distribution of the maximum of a gaussian process
An explicit representation of the extended Skorokhod map with two time-dependent boundaries.