Interacting random walk in a dynamical random environment. I. Decay of correlations
Intermittent estimation for finite alphabet finitarily Markovian processes with exponential tails
We give some estimation schemes for the conditional distribution and conditional expectation of the the next output following the observation of the first outputs of a stationary process where the random variables may take finitely many possible values. Our schemes are universal in the class of finitarily Markovian processes that have an exponential rate for the tail of the look back time distribution. In addition explicit rates are given. A necessary restriction is that the scheme proposes an...
Internal DLA in a random environment
Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry.
We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general F-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide criteria for these Sobolev type inequalities and for related properties. In particular, we implement in the context of probability measures the ideas of Maz'ja's capacity theory, and present equivalent forms relating the capacity of sets to their measure. Orlicz hypercontractivity efficiently describes the...
Interpolation and forecasting in Brownian functions of two parameters.
Interpolation and forecasting in Poisson's processes.
Interpolation of random functions.
Interprétation d'un calcul de H. Tanaka en théorie générale des processus
Intersection probabilities for a chordal SLE path and a semicircle.
Intertwining of birth-and-death processes
It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the negatives of the eigenvalues of the stopped process. Recently, Diaconis and Miclo have given a probabilistic proof of this fact by constructing a coupling between a general birth-and-death process and a process whose birth rates are the negatives of the eigenvalues,...
Intrinsic Stochastic Processes.
Introduction au calcul stochastique
Invariance of Poisson measures under random transformations
We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for adapted and anticipating Poisson stochastic integrals, and is inspired by the method of Üstünel and Zakai (Probab. Theory Related Fields103 (1995) 409–429) on the Wiener space, although the corresponding algebra is more complex than in the Wiener case. The examples...
Invariance of spectral type of a stochastic process with respect to transformation of time.
Invariance principle for Mott variable range hopping and other walks on point processes
We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the -power of the jump length and depend on the energy marks via a Boltzmann-like factor. The case corresponds to the phonon-induced Mott variable range hopping in disordered solids in the regime of strong Anderson localization. We prove that for almost every realization of the marked process, the diffusively rescaled random walk, with an arbitrary start point, converges to...
Invariance principle in a bilinear model with weak nonlinearity.
Invariance principle, multifractional gaussian processes and long-range dependence
This paper is devoted to establish an invariance principle where the limit process is a multifractional gaussian process with a multifractional function which takes its values in (1/2, 1). Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional brownian motion.
Invariance principles for random walks conditioned to stay positive
Let {Snbe a random walk in the domain of attraction of a stable law , i.e. there exists a sequence of positive real numbers ( an) such that Sn/anconverges in law to . Our main result is that the rescaled process (S⌊nt⌋/an, t≥0), when conditioned to stay positive, converges in law (in the functional sense) towards the corresponding stable Lévy process conditioned to stay positive. Under some additional assumptions, we also prove a related invariance principle for the random walk killed at its first...
Invariant measures and a stability theorem for locally Lipschitz stochastic delay equations
We consider a stochastic delay differential equation with exponentially stable drift and diffusion driven by a general Lévy process. The diffusion coefficient is assumed to be locally Lipschitz and bounded. Under a mild condition on the large jumps of the Lévy process, we show existence of an invariant measure. Main tools in our proof are a variation-of-constants formula and a stability theorem in our context, which are of independent interest.
Invariant measures of the pair: state, approximate filtering process