Search results for "probability"
showing 10 items of 3417 documents
On BLD-mappings with small distortion
2021
We show that every $$L$$ -BLD-mapping in a domain of $$\mathbb {R}^{n}$$ is a local homeomorphism if $$L < \sqrt{2}$$ or $$K_I(f) < 2$$ . These bounds are sharp as shown by a winding map.
A C0-Semigroup of Ulam Unstable Operators
2020
The Ulam stability of the composition of two Ulam stable operators has been investigated by several authors. Composition of operators is a key concept when speaking about C0-semigroups. Examples of C0-semigroups formed with Ulam stable operators are known. In this paper, we construct a C0-semigroup (Rt)t&ge
Ulam Stability for the Composition of Operators
2020
Working in the setting of Banach spaces, we give a simpler proof of a result concerning the Ulam stability of the composition of operators. Several applications are provided. Then, we give an example of a discrete semigroup with Ulam unstable members and an example of Ulam stable operators on a Banach space, such that their sum is not Ulam stable. Another example is concerned with a C 0 -semigroup ( T t ) t &ge
Connexion markovienne, courbure et formule de Weitzenböck sur l'espace des chemins riemanniens
2001
Resume Nous considerons la connexion markovienne sur l'espace des chemins riemanniens. Le tenseur de courbure est calcule explicitement et une formula de Weitzenbock est etablie.
Algebraic aspects and coherence conditions for conjoined and disjoined conditionals
2019
We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known properties, valid in the case of unconditional events, still hold in our approach to logical operations among conditional events. In particular we prove a decomposition formula and a related additive property. Then, we introduce the set of conditional constituents generated by $n$ conditional events and we show that they satisfy the basic properties valid in the case of unconditional events. We obtain a generalized inclusion-exclusion formula and we prove a …
Fractional Laplacians in bounded domains: Killed, reflected, censored, and taboo Lévy flights.
2018
The fractional Laplacian $(- \Delta)^{\alpha /2}$, $\alpha \in (0,2)$ has many equivalent (albeit formally different) realizations as a nonlocal generator of a family of $\alpha $-stable stochastic processes in $R^n$. On the other hand, if the process is to be restricted to a bounded domain, there are many inequivalent proposals for what a boundary-data respecting fractional Laplacian should actually be. This ambiguity holds true not only for each specific choice of the process behavior at the boundary (like e.g. absorbtion, reflection, conditioning or boundary taboos), but extends as well to its particular technical implementation (Dirchlet, Neumann, etc. problems). The inferred jump-type …
Toeplitz band matrices with small random perturbations
2021
We study the spectra of $N\times N$ Toeplitz band matrices perturbed by small complex Gaussian random matrices, in the regime $N\gg 1$. We prove a probabilistic Weyl law, which provides an precise asymptotic formula for the number of eigenvalues in certain domains, which may depend on $N$, with probability sub-exponentially (in $N$) close to $1$. We show that most eigenvalues of the perturbed Toeplitz matrix are at a distance of at most $\mathcal{O}(N^{-1+\varepsilon})$, for all $\varepsilon >0$, to the curve in the complex plane given by the symbol of the unperturbed Toeplitz matrix.
SOME RELATIONS BETWEEN BOUNDED BELOW ELLIPTIC OPERATORS AND STOCHASTIC ANALYSIS
2019
International audience; We apply Malliavin Calculus tools to the case of a bounded below elliptic rightinvariant Pseudodifferential operators on a Lie group. We give examples of bounded below pseudodifferential elliptic operators on R d by using the theory of Poisson process and the Garding inequality. In the two cases, there is no stochastic processes besides because the considered semi-groups do not preserve positivity.
Stability of the Fixed Point Property for Nonexpansive Mappings
2001
In 1971 Zidler [Zi 71] showed that every separable Banach space (X, ‖·‖) admits an equivalent renorming, (X, ‖·‖0), which is uniformly convex in every direction (UCED), and consequently it has weak normal structure and so the weak fixed point property (WFPP) [D-J-S 71].
Traces of weighted function spaces: dyadic norms and Whitney extensions
2017
The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well adapted to extending functions using the Whitney extension operator.