DSpace Collection:
http://hdl.handle.net/10077/4161
20210923T09:52:30Z

An analytical introduction to stochastic differential equations: Part I  the Langevin equation
http://hdl.handle.net/10077/4265
Title: An analytical introduction to stochastic differential equations: Part I  the Langevin equation
Authors: ClĂ©ment, 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 RiemannStieltjes 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.
20000101T00:00:00Z

Continuous dependence results for an inverse problem in the theory of combustion of materials with memory
http://hdl.handle.net/10077/4264
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.
20000101T00:00:00Z

Filters and pathwise connectification
http://hdl.handle.net/10077/4263
Title: Filters and pathwise connectification
Authors: Costantini, Camillo; Fedeli, Alessandro; Le Donne, Attilio
Abstract: Let p be a free openfilter 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.
20000101T00:00:00Z

Relaxed parabolic problems
http://hdl.handle.net/10077/4262
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 righthand 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.
20000101T00:00:00Z