Les changements de temps en théorie générale des processus
Lévy processes conditioned on having a large height process
In the present work, we consider spectrally positive Lévy processes not drifting to and we are interested in conditioning these processes to reach arbitrarily large heights (in the sense of the height process associated with ) before hitting . This way we obtain a new conditioning of Lévy processes to stay positive. The (honest) law of this conditioned process (starting at ) is defined as a Doob -transform via a martingale. For Lévy processes with infinite variation paths, this martingale...
Manifold indexed fractional fields
(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.
Manifold indexed fractional fields∗
(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.
Maximal brownian motions
Let Z=(X, Y) be a planar brownian motion, the filtration it generates, andBa linear brownian motion in the filtration . One says thatB(or its filtration) is maximal if no other linear -brownian motion has a filtration strictly bigger than that ofB. For instance, it is shown in [In Séminaire de Probabilités XLI 265–278 (2008) Springer] that B is maximal if there exists a linear brownian motion C independent of B and such that the planar brownian motion (B, C) generates the same filtration asZ....
Maximal inequalities via bracketing with adaptive truncation
Mesurabilité des débuts et théorème de section : le lot à la portée de toutes les bourses
Multivariate Markov Families of Copulas
For the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples...
Note sur les processus d'Ornstein-Uhlenbeck
On a class of processes with multiplicity .
On a construction of majorizing measures on subsets of ℝⁿ with special metrics
We consider processes Xₜ with values in and “time” index t in a subset A of the unit cube. A natural condition of boundedness of increments is assumed. We give a full characterization of the domains A for which all such processes are a.e. continuous. We use the notion of Talagrand’s majorizing measure as well as geometrical Paszkiewicz-type characteristics of the set A. A majorizing measure is constructed.
On certain almost brownian filtrations
On certain probabilities equivalent to Wiener measure, d'après Dubins, Feldman, Smorodinsky and Tsirelson
On convex stochastic processes.
On countable dense random sets
On Markovian traffic with applications to TES processes.
On Paszkiewicz-type criterion for a.e. continuity of processes in -spaces
In this paper we consider processes Xₜ with values in , p ≥ 1 on subsets T of a unit cube in ℝⁿ satisfying a natural condition of boundedness of increments, i.e. a process has bounded increments if for some non-decreasing f: ℝ₊ → ℝ₊ ||Xₜ-Xₛ||ₚ ≤ f(||t-s||), s,t ∈ T. We give a sufficient criterion for a.s. continuity of all processes with bounded increments on subsets of a given set T. This criterion turns out to be necessary for a wide class of functions f. We use a geometrical Paszkiewicz-type...
On some properties of J-convex stochastic processes.
On the Ray topology
On Vershik's standardness criterion and Tsirelson's notion of cosiness