Strong-viscosity Solutions: Semilinear Parabolic PDEs and Path-dependent PDEs

The aim of the present work is the introduction of a viscosity type solution, called strong-viscosity solution to distinguish it from the classical one, with the following peculiarities: it is a purely analytic object; it can be easily adapted to more general equations than classical partial differential equations. First, we introduce the notion of strong-viscosity solution for semilinear parabolic partial differential equations, defining it, in a few words, as the pointwise limit of classical solutions to perturbed semilinear parabolic partial differential equations; we compare it with the standard definition of viscosity solution. Afterwards, we extend the concept of strong-viscosity solution to the case of semilinear parabolic path-dependent partial differential equations, providing an existence and uniqueness result.Comment: arXiv admin note: text overlap with arXiv:1401.503

Functional it{\^o} versus banach space stochastic calculus and strict solutions of semilinear path-dependent equations

Functional It\^o calculus was introduced in order to expand a functional $F(t, X\_{\cdot+t}, X\_t)$ depending on time $t$, past and present values of the process $X$. Another possibility to expand $F(t, X\_{\cdot+t}, X\_t)$ consists in considering the path $X\_{\cdot+t}=\{X\_{x+t},\,x\in[-T,0]\}$ as an element of the Banach space of continuous functions on $C([-T,0])$ and to use Banach space stochastic calculus. The aim of this paper is threefold. 1) To reformulate functional It\^o calculus, separating time and past, making use of the regularization procedures which matches more naturally the notion of horizontal derivative which is one of the tools of that calculus. 2) To exploit this reformulation in order to discuss the (not obvious) relation between the functional and the Banach space approaches. 3) To study existence and uniqueness of smooth solutions to path-dependent partial differential equations which naturally arise in the study of functional It\^o calculus. More precisely, we study a path-dependent equation of Kolmogorov type which is related to the window process of the solution to an It\^o stochastic differential equation with path-dependent coefficients. We also study a semilinear version of that equation.Comment: This paper is a substantial improvement with additional research material of the first part of the unpublished paper arXiv:1401.503

Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations

The paper reminds the basic ideas of stochastic calculus via regularizations in Banach spaces and its applications to the study of strict solutions of Kolmogorov path dependent equations associated with "windows" of diffusion processes. One makes the link between the Banach space approach and the so called functional stochastic calculus. When no strict solutions are available one describes the notion of strong-viscosity solution which alternative (in infinite dimension) to the classical notion of viscosity solution.Comment: arXiv admin note: text overlap with arXiv:1401.503

A regularization approach to functional It\^o calculus and strong-viscosity solutions to path-dependent PDEs

First, we revisit functional It\^o/path-dependent calculus started by B. Dupire, R. Cont and D.-A. Fourni\'e, using the formulation of calculus via regularization. Relations with the corresponding Banach space valued calculus introduced by C. Di Girolami and the second named author are explored. The second part of the paper is devoted to the study of the Kolmogorov type equation associated with the so called window Brownian motion, called path-dependent heat equation, for which well-posedness at the level of classical solutions is established. Then, a notion of strong approximating solution, called strong-viscosity solution, is introduced which is supposed to be a substitution tool to the viscosity solution. For that kind of solution, we also prove existence and uniqueness. The notion of strong-viscosity solution motivates the last part of the paper which is devoted to explore this new concept of solution for general semilinear PDEs in the finite dimensional case. We prove an equivalence result between the classical viscosity solution and the new one. The definition of strong-viscosity solution for semilinear PDEs is inspired by the notion of "good" solution, and it is based again on an approximating procedure

Storie autobiografiche e autobiografia romanzata: traduzione e commento di alcuni racconti e dell'autobiografia di Arthur Machen

Questa tesi di laurea magistrale propone la traduzione di alcuni racconti fantastici e dell’autobiografia (Far Off Things) del gallese Arthur Machen (1863-1947). Dopo un breve sguardo alla biografia, alle opere, alla ricezione e fortuna dell’autore e alla sua poetica, il commento critico metterà in risalto prima le caratteristiche narratologiche e stilistiche dei racconti e poi l’importanza e i contenuti dell’autobiografia. Infine, il commento traduttologico evidenzierà i principali ostacoli alla traduzione di opere lontane dal lettore italiano d’oggi dal punto di vista sia temporale sia culturale

Davenant's The Law Against Lovers: Rewriting Shakespeare in early Restoration theatre

L'elaborato finale tratta uno dei primi adattamenti shakespeariani del periodo della restaurazione: The Law Against Lovers (1662, La legge contro gli amanti). L'opera, scritta da Sir William Davenant (figura chiave del teatro del periodo immediatamente precedente e successivo all'Interregno), adatta due opere del Bardo: Misura per misura e Molto rumore per nulla. Si analizzano qui le sue caratteristiche salienti, le innovazioni e le differenze rispetto ai due testi di partenza, sottolineando l'abilità di Davenant nello sfruttare gli elementi di successo del teatro (attrici, musica e danza, effetti scenici). Si traccia insomma una analisi mettendo in luce da una parte il contesto (letterario, teatrale, con le sue innovazioni, e politico), dall'altra l'operazione di Davenant sui testi di Shakespeare, che stravolge il senso originale, soprattutto da un punto di vista morale. This essay analyses The Law Against Lovers, a conflation of two Shakespearean works: Measure for Measure and Much Ado About Nothing. It is one of the very first adaptations of the Restoration period (1662), and one of the most peculiar, too. We highlight Davenant's ability to use the innovations of the theatre of the time (actresses, music and dance, theatrical effects) to achieve success (although in the end we cannot be sure whether this adaptation was actually successful). To conclude, one the one hand we have analysed the context of this adaptation (from a literary and also political perspective), and on the other hand we have analysed the changes carried out by Davenant to the two source texts, in order to prove that this adaptation is by no means «a sad puzzle» as some critics have said; it is instead a «good play», and a perfect example of the way Restoration adapters considered Shakespeare

The Causes and Consequences of Venture Capital Financing. An Analysis based on a Sample of Italian Firms

The analysis of the determinants and the effects on firm performance of venture capital finance for a sample of Italian enterprises indicates that small, young and more innovative firms are more likely to be financed by a venture capitalist. Our results confirm that venture capital can help reduce financial constraints for firms that are more difficult for external investors to evaluate. We also show that larger firms resort to venture capitalists when their indebtedness with banks is high and we find evidence that venture capital financing is more frequent after periods of high growth and investment, a result that points to the advisory role of the venture capitalist. A novel result emerges; venture capital also finances firms with multiple banking relationships. In the presence of multiple lending, banks could have greater difficulty monitoring firms with asymmetric information; moreover, if firms default, banks are likely to have a weaker bargaining position. In these cases, the amount of bank credit is probably near its limit and firms need to resort to venture capital, a contract that reduces the amount of guarantees needed to access external finance.Venture capital, Private equity

Spontaneous intracranial hypotension : two steroid-responsive cases

Purpose: Spontaneous intracranial hypotension (SIH) is characterised by orthostatic headache, low cerebrospinal fluid pressure and diffuse pachymeningeal enhancement after intravenous gadolinium contrast administration. Magnetic resonance imaging (MRI) often plays a crucial role for correct diagnosis. Case description: We described two similar cases of SIH, whose clinical and imaging features are typical for this pathology. At MRI brain scan, both patients showed diffuse and intense pachymeningeal enhancement and moderate venous distension and epidural vein engorgement. The two patients were treated with bed rest and oral steroid therapy, with complete and long-lasting symptomatic relief. Conclusions: Orthostatic nature of headache is the most indicative clinical feature suggesting SIH; contrast-enhanced MRI provides definite imaging diagnostic findings. Conservative treatment coupled to steroid therapy is often sufficient to obtain complete disappearance of symptoms

Knowledge-Intensive Processes: Characteristics, Requirements and Analysis of Contemporary Approaches

Engineering of knowledge-intensive processes (KiPs) is far from being mastered, since they are genuinely knowledge- and data-centric, and require substantial flexibility, at both design- and run-time. In this work, starting from a scientific literature analysis in the area of KiPs and from three real-world domains and application scenarios, we provide a precise characterization of KiPs. Furthermore, we devise some general requirements related to KiPs management and execution. Such requirements contribute to the definition of an evaluation framework to assess current system support for KiPs. To this end, we present a critical analysis on a number of existing process-oriented approaches by discussing their efficacy against the requirements