1,721,334 research outputs found
2D vortex motion of an incompressible ideal fluid: the Koopman-von Neumann approach
No full textAn incompressible ideal fluid in the two-dimensional torus (i.e. the Euler equation in a rectangle with periodic boundary conditions) is considered. The flow for a vorticity field concentrated in any finite number of points is analyzed. A compound Poisson measure Pi, invariant for this flow, is introduced. The Hilbert space L-2(Pi) and the properties of the corresponding L-2-flow are investigated. In particular it is proven that the corresponding generator is Markov unique
Large deviation principle for spatial economic growth model on networks
No full textIn this paper we study a spatially structured economic growth model on a finite network in the presence of a Wiener noise acting on the system. We consider an extension of the Solow's model under the assumption of Lipschitz type for the production function and uniform boundedness of the productivity operator. Our interest is mainly set in studying the small noise asymptotics of the system. In our model, we obtain bounds on the probability that the logarithm of the capital stock will differ from its deterministic steady state level by a given amount. We show that this probability decays exponentially with the intensity of the noise.(c) 2022 Elsevier B.V. All rights reserved
Homogenization in random Dirichlet forms
No full textA general diffusion process in a random medium associated with
a random Dirichlet form with nonsmooth and nonbounded coefficients is
considered, as drift transformation of a starting diffusion process in a
random medium, with random infinitesimal generator in divergence form. The
corresponding homogenization problem is studied and conditions are found
such that the suitably rescaled original process converges weakly, as the scaling
parameter is sent to the limit, to a diffusion process with constant coefficients.
Stochastic analysis associated with Dirichlet forms is used in the proof
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De Rham complex over product manifolds: Dirichlet forms and stochastic dynamics
No full textThe Riemann zeta in terms of the dilogarithm
No full textWe give a representation of the classical Riemann ζ-function in the half plane Res > 0 in terms of a Mellin transform involving the real part of the dilogarithm function with an argument on the unit circle (associated Clausen Gl2-function). We also derive corresponding representations involving the derivatives of the Gl2-function. A generalized symmetrized Müntz-type formula is also derived. For a special choice of test functions it connects to our integral representation of the ζ-function, providing also a computation of a concrete Mellin transform. Certain formulae involving series of zeta functions and gamma functions are also derived
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