http://www.openstarts.units.it:80/dspace/handle/10077/4161 2013-05-24T21:54:38Z 2013-05-24T21:54:38Z Clément, Ph. van Gaans, O. W. http://www.openstarts.units.it:80/dspace/handle/10077/4265 2011-04-08T23:34:48Z 2000-01-01T00:00:00Z

Title: An analytical introduction to stochastic differential equations: Part I - the Langevin equation Authors: Clément, Ph.; van Gaans, O. W. Abstract: We present an introduction to the theory of stochastic differential equations, motivating and explaining ideas from the point of view of analysis. First the notion of white noise is developed, introducing at the same time probabilistic tools. Then the one dimensional Langevin equation is formulated as a deterministic integral equation with a parameter. Its solution leads to stochastic convolution, which is defined as a Riemann-Stieltjes integral. It is shown that the parameter dependence yields a Gaussian system, of which the means and covariances arde computed. We conclude by introducing briefly the notion of invariant measure and the associated Kolmogorov equations. Type: Articolo

2000-01-01T00:00:00Z Colombo, Fabrizio http://www.openstarts.units.it:80/dspace/handle/10077/4264 2011-04-08T23:34:53Z 2000-01-01T00:00:00Z

Title: Continuous dependence results for an inverse problem in the theory of combustion of materials with memory Authors: Colombo, Fabrizio Abstract: We prove theorems of continuous dependence on the data for both direct and inverse problems for semilinear integrodifferential equations. Such results are applied to the specific case of the combustion of a material with memory. Type: Articolo

2000-01-01T00:00:00Z Costantini, Camillo Fedeli, Alessandro Le Donne, Attilio http://www.openstarts.units.it:80/dspace/handle/10077/4263 2011-07-20T10:10:37Z 2000-01-01T00:00:00Z

Title: Filters and pathwise connectification Authors: Costantini, Camillo; Fedeli, Alessandro; Le Donne, Attilio Abstract: Let p be a free open-filter on a Hausdorff space X. In this paper we investigate when $X \cup {p}$ can be densely embedded in a pathwise connected $T_2$-space. The main part of the paper is devoted to the cases where X is the rational or the real line. Type: Articolo

2000-01-01T00:00:00Z Smolka, Maciej http://www.openstarts.units.it:80/dspace/handle/10077/4262 2012-11-26T09:09:07Z 2000-01-01T00:00:00Z

Title: Relaxed parabolic problems Authors: Smolka, Maciej Abstract: Let $G_{n}$ be a sequence of open subsets of a given open and bounded $\Omega\subset\mathbb{R}^{N}$. We study the asymptotic behaviour of the solutions of parabolic equations $u_{n}'+Au_{n}=f_{n}\:\textrm{on}\: G_{n}$. Assuming that the right-hand sides $f_{n}$ and the initial conditions converge in a proper way we find the form of the limit problem without any additional hypothesis on $G_{n}$. Our method is based on the notion of elliptic $\gamma^{A}$-convergence. Type: Articolo

2000-01-01T00:00:00Z