On the time evolution of Bernstein processes associated with a class of parabolic equations

In this article dedicated to the memory of Igor D. Chueshov, I first summarize in a few words the joint results that we obtained over a period of six years regarding the long-time behavior of solutions to a class of semilinear stochastic parabolic partial differential equations. Then, as the beautiful interplay between partial differential equations and probability theory always was close to Igor's heart, I present some new results concerning the time evolution of certain Markovian Bernstein processes naturally associated with a class of deterministic linear parabolic partial differential equations. Particular instances of such processes are certain conditioned Ornstein-Uhlenbeck processes, generalizations of Bernstein bridges and Bernstein loops, whose laws may evolve in space in a non trivial way. Specifically, I examine in detail the time development of the probability of finding such processes within two-dimensional geometric shapes exhibiting spherical symmetry. I also define a Faedo-Galerkin scheme whose ultimate goal is to allow approximate computations with controlled error terms of the various probability distributions involved

From Predators to Icons: Exposing the Myth of the Business Hero

[ Excerpted from Forword by John R. Kimberly] From Predators to Icons takes us on a provocative and nuanced journey through the business practices of a number of individuals and the companies they built and shows how they navigated through this volatile mix to achieve extraordinary success in their undertakings. In an era in which we are obsessed with rankings of everything from colleges and universities to hospitals to tennis players, we tend to focus on the end result—who is number 1?—and much less on the means: how did they get there? In an era when we are fascinated by stories of leaders as heroes and by the lives of the rich and famous, we tend to let the gloss of the material trappings of success blind us to questions of their origins. In the work they report here, Villette and Vuillermot use the lens of social science as a vehicle for unpacking the roots of extraordinary success in business, for analyzing how success was achieved. They have accumulated evidence from a variety of sources, including the myriad biographies—authorized and unauthorized—of business icons, to build their comparative analysis of the practices of thirty-two businessmen from Europe and North America, of how their wealth was built, and of the common threads that characterize the roots of success across geographies, across industries, and across time. Their approach is highly original, and the data they assemble are wide-ranging. They are well aware of both the promise and the limitations of their data and are careful to discuss both. Ultimately, it is up to each of us to judge the credibility of both the empirical foundations on which their analysis is built and the conclusions they reach, the messages they send. But theirs is an impressive undertaking and needs to be taken seriously

Mild Solutions for a Class of Fractional SPDEs and Their Sample Paths

In this article we introduce and analyze a notion of mild solution for a class of non-autonomous parabolic stochastic partial differential equations defined on a bounded open subset $D\subset\mathbb{R}^{d}$ and driven by an infinite-dimensional fractional noise. The noise is derived from an $L^{2}(D)$-valued fractional Wiener process $W^{H}$ whose covariance operator satisfies appropriate restrictions; moreover, the Hurst parameter $H$ is subjected to constraints formulated in terms of $d$ and the H\"{o}lder exponent of the derivative $h^\prime$ of the noise nonlinearity in the equations. We prove the existence of such solution, establish its relation with the variational solution introduced in \cite{nuavu} and also prove the H\"{o}lder continuity of its sample paths when we consider it as an $L^{2}(D)$--valued stochastic processes. When $h$ is an affine function, we also prove uniqueness. The proofs are based on a relation between the notions of mild and variational solution established in Sanz-Sol\'e and Vuillermot 2003, and adapted to our problem, and on a fine analysis of the singularities of Green's function associated with the class of parabolic problems we investigate. An immediate consequence of our results is the indistinguishability of mild and variational solutions in the case of uniqueness.Comment: 37 page

On some Gaussian Bernstein processes in RN and the periodic Ornstein-Uhlenbeck process

In this article we prove new results regarding the existence of Bernstein processes associated with the Cauchy problem of certain forward-backward systems of decoupled linear deterministic parabolic equations defined in Euclidean space of arbitrary dimension N, whose initial and final conditions are positive measures. We concentrate primarily on the case where the elliptic part of the parabolic operator is related to the Hamiltonian of an isotropic system of quantum harmonic oscillators. In this situation there are many Gaussian processes of interest whose existence follows from our analysis, including N-dimensional stationary and non-stationary Ornstein-Uhlenbeck processes, as well as a Bernstein bridge which may be interpreted as a Markovian loop in a particular case. We also introduce a new class of stationary non-Markovian processes which we eventually relate to the N-dimensional periodic Ornstein-Uhlenbeck process, and which is generated by a one-parameter family of non-Markovian probability measures. In this case our construction requires an infinite hierarchy of pairs of forward-backward heat equations associated with the pure point spectrum of the elliptic part, rather than just one pair in the Markovian case. We finally stress the potential relevance of these new processes to statistical mechanics, the random evolution of loops and general pattern theory.Comment: Research articl

« Du secret des affaires à la politique de communication (L'exemple de quelques grandes entreprises industrielles françaises et de leur presse interne, des années 1930 à nos jours) »

Après avoir longtemps été un espace de rationalisation mécanique, l'entreprise se transforme en système relationnel. Le journal d'entreprise est un support de communication sociale au service de la gestion des ressources humaines. En ce sens, il produit des representations, mais c'est aussi un outil de management. L'objectif est de dater les changements dans la politique de communication avec le personnel de quelques grandes entreprises par le biais de la presse interne. Quand a-t-on mis fin à l'idée du secret absolu des affaires pour développer des outils d'information ? Le public ciblé est limité au personnel des entreprises à travers quelques études de cas de vieilles compagnies industrielles françaises de premier plan : Saint-Gobain, Pont-à-Mousson, Schneider et leurs filiales

« Du secret des affaires à la politique de communication (L'exemple de quelques grandes entreprises industrielles françaises et de leur presse interne, des années 1930 à nos jours) »

Après avoir longtemps été un espace de rationalisation mécanique, l'entreprise se transforme en système relationnel. Le journal d'entreprise est un support de communication sociale au service de la gestion des ressources humaines. En ce sens, il produit des representations, mais c'est aussi un outil de management. L'objectif est de dater les changements dans la politique de communication avec le personnel de quelques grandes entreprises par le biais de la presse interne. Quand a-t-on mis fin à l'idée du secret absolu des affaires pour développer des outils d'information ? Le public ciblé est limité au personnel des entreprises à travers quelques études de cas de vieilles compagnies industrielles françaises de premier plan : Saint-Gobain, Pont-à-Mousson, Schneider et leurs filiales.Histoire, communication, entreprises

On the asymptotic behavior of solutions to a class of grand canonical master equations

In this article, we investigate the long-time behavior of solutions to a class of infinitely many master equations defined from transition rates that are suitable for the description of a quantum system approaching thermodynamical equilibrium with a heat bath at fixed temperature and a reservoir consisting of one species of particles characterized by a fixed chemical potential.We do so by proving a result which pertains to the spectral resolution of the semigroup generated by the equations, whose infinitesimal generator is realized as a trace-class self-adjoint operator defined in a suitably weighted sequence space. This allows us to prove the existence of global solutions which all stabilize toward the grand canonical equilibrium probability distribution as the time variable becomes large, some of them doing so exponentially rapidly but not all. When we set the chemical potential equal to zero, the stability statements continue to hold in the sense that all solutions converge toward the Gibbs probability distribution of the canonical ensemble which characterizes the equilibrium of the given system with a heat bath at fixed temperature