Introduction au calcul stochastique
Invariance principle in a bilinear model with weak nonlinearity.
Invariance principles for Brownian intersection local time and polymer measures.
Invariance principles for spatial multitype Galton–Watson trees
We prove that critical multitype Galton–Watson trees converge after rescaling to the brownian continuum random tree, under the hypothesis that the offspring distribution is irreducible and has finite covariance matrices. Our study relies on an ancestral decomposition for marked multitype trees, and an induction on the number of types. We then couple the genealogical structure with a spatial motion, whose step distribution may depend on the structure of the tree in a local way, and show that the...
Invariant densities of random maps have lower bounds on their supports.
Invariant local Dirichlet forms on locally compact groups
Invariant measure for some differential operators and unitarizing measure for the representation of a Lie group. Examples in finite dimension
Consider a Lie group with a unitary representation into a space of holomorphic functions defined on a domain 𝓓 of ℂ and in L²(μ), the measure μ being the unitarizing measure of the representation. On finite-dimensional examples, we show that this unitarizing measure is also the invariant measure for some differential operators on 𝓓. We calculate these operators and we develop the concepts of unitarizing measure and invariant measure for an OU operator (differential operator associated to...
Invariant measures for Burgers equation with stochastic forcing.
Invariant measures for iterated function systems
A new criterion for the existence of an invariant distribution for Markov operators is presented. Moreover, it is also shown that the unique invariant distribution of an iterated function system is singular with respect to the Hausdorff measure.
Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities
Invariant measures for nonexpansive Markov operators on Polish spaces [Book]
Invariant measures for random dynamical systems [Book]
Invariant measures related with randomly connected Poisson driven differential equations
We consider the stochastic differential equation (1) for t ≥ 0 with the initial condition u(0) = x₀. We give sufficient conditions for the existence of an invariant measure for the semigroup corresponding to (1). We show that the existence of an invariant measure for a Markov operator P corresponding to the change of measures from jump to jump implies the existence of an invariant measure for the semigroup describing the evolution of measures along trajectories and vice versa.
Invariant probabilities for Feller-Markov chains.
Invariant wedges for a two-point reflecting Brownian motion and the “hot spots” problem.
Inverse limits need not exist in the category of compact spaces and Feller kernels: a counterexample
Inverspositive Operatoren und Taubersätze in der Erneuerungstheorie.
Irreducible Markov systems on Polish spaces
Contractive Markov systems on Polish spaces which arise from graph directed constructions of iterated function systems with place dependent probabilities are considered. It is shown that their stability may be studied using the concentrating methods developed by the second author [Dissert. Math. 415 (2003)]. In this way Werner's results obtained in a locally compact case [J. London Math. Soc. 71 (2005)] are extended to a noncompact setting.
Isolated points of some sets of bounded cosine families, bounded semigroups, and bounded groups on a Banach space
We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space 𝓛(X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family whose members are all scalar multiples of the identity operator. We also show that if the sets of all bounded...
Isomorphic random Bernoulli shifts
We develop a relative isomorphism theory for random Bernoulli shifts by showing that any random Bernoulli shifts are relatively isomorphic if and only if they have the same fibre entropy. This allows the identification of random Bernoulli shifts with standard Bernoulli shifts.