Caractéristiques locales des semi-martingales et changements de probabilités
Carthaginian enlargement of filtrations
This work is concerned with the theory of initial and progressive enlargements of a reference filtration F with a random timeτ. We provide, under an equivalence assumption, slightly stronger than the absolute continuity assumption of Jacod, alternative proofs to results concerning canonical decomposition of an F -martingale in the enlarged filtrations. Also, we address martingales’ characterization in the enlarged filtrations in terms of martingales in the reference filtration, as well as predictable...
Cauchy approximation for sums of independent random variables.
Cauchy's principal value of local times of Lévy processes with no negative jumps via continuous branching processes.
Central and non-central limit theorems for weighted power variations of fractional brownian motion
In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q≥2 of the fractional brownian motion with Hurst parameter H∈(0, 1), where q is an integer. The central limit holds for 1/2q<H≤1−1/2q, the limit being a conditionally gaussian distribution. If H<1/2q we show the convergence in L2 to a limit which only depends on the fractional brownian motion, and if H>1−1/2q we show the convergence in L2 to a stochastic integral...
Central limit theorem for Gibbsian U-statistics of facet processes
A special case of a Gibbsian facet process on a fixed window with a discrete orientation distribution and with increasing intensity of the underlying Poisson process is studied. All asymptotic joint moments for interaction U-statistics are calculated and the central limit theorem is derived using the method of moments.
Central limit theorem for Hölder processes on -unit cube
We consider a sequence of stochastic processes with continuous trajectories and we show conditions for the tightness of the sequence in the Hölder space with a parameter .
Central limit theorem for random measures generated by stationary processes of compact sets
Random measures derived from a stationary process of compact subsets of the Euclidean space are introduced and the corresponding central limit theorem is formulated. The result does not require the Poisson assumption on the process. Approximate confidence intervals for the intensity of the corresponding random measure are constructed in the case of fibre processes.
Central limit theorem for sampled sums of dependent random variables
We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to dependent random variables sampled by a -valued transient random walk. This extends the results obtained by [N. Guillotin-Plantard and D. Schneider, Stoch. Dynamics3 (2003) 477–497]. An application to parametric estimation by random sampling is also provided.
Central limit theorem for solutions of random initialized differential equations: a simple proof.
Central limit theorems for the products of random matrices sampled by a random walk.
Chaînes de Markov à dérive stable et loi des grands nombres sur les hypergroupes
Chains with complete connections and one-dimensional Gibbs measures.
Changements de temps et intégrales stochastiques
Changing the branching mechanism of a continuous state branching process using immigration
We consider an initial population whose size evolves according to a continuous state branching process. Then we add to this process an immigration (with the same branching mechanism as the initial population), in such a way that the immigration rate is proportional to the whole population size. We prove this continuous state branching process with immigration proportional to its own size is itself a continuous state branching process. By considering the immigration as the apparition of a new type,...
Changing time for two-parameter strong martingales
Chaos expansions and local times.
In this note we prove that the Local Time at zero for a multiparametric Wiener process belongs to the Sobolev space Dk - 1/2 - ε,2 for any ε > 0. We do this computing its Wiener chaos expansion. We see also that this expansion converges almost surely. Finally, using the same technique we prove similar results for a renormalized Local Time for the autointersections of a planar Brownian motion.
Chaotic behavior of infinitely divisible processes
The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.
Chaoticity on a stochastic interval
Character theory of symmetric groups, analysis of long relators, and random walks.