3,175 research outputs found
Hardening the BMV conjecture
No full textDiese Arbeit basiert auf den Resultaten der Publikation "A hyper-geometric approach to the BMV-conjecture" von Michael Drmota, Walter Schachermayer und Josef Teichmann. Zuerst wird die Vermutung und einige bekannten Fakten darüber präsentiert, gefolgt von den Resultaten der oben genannten Publikation, speziell eine Formel zur Berechnung der Dichtefunktion eines Maßes auf den nicht negativen reellen Zahlen. Positivität dieses Maßes würde die BMV-Vermutung im reellen dreidimensionalen Fall beweisen. Die numerische Implementierung der oben genannten Formel und die dafür notwendigen Abschätzungen bilden den Hauptteil der Arbeit und werden hier präsentiert.This work is based on the results of the paper ``A hyper-geometric approach to the BMV-conjecture'' by Michael Drmota, Walter Schachermayer and Josef Teichmann. First I will introduce the conjecture itself and some basic facts about it followed by the results of the aforementioned paper, especially a formula to calculate the density function of a measure on the non-negative real numbers. This measure respectively its density function plays the main role, because if it turns out to be positive, in this case it would prove the BMV conjecture in a special case. And that's actually what this is all about, mainly to calculate the density function based on the provided formula as a base or starting point for further investigations whether it's possible to find negative function values or not
The Reform Catholic Josef Dobrovský
No full textReformní katolík Josef Dobrovský The Reform Catholic Josef Dobrovský Josef Táborský The goal of this dissertation thesis is to introduce Josef Dobrovský as a priest influenced by the Enlightenment and participating in reformative effort in Catholic church of 18th century. Author of this dissertation has not focused on Josef Dobrovský's excellent scientific work but rather on the importance of Josef Dobrovský as both the scholar and the the man oriented towards the Christian faith and questions connected with it
Signature SDEs from an affine and polynomial perspective
No full textSignature stochastic differential equations (SDEs) constitute a large class of stochas- tic processes, here driven by Brownian motions, whose characteristics are entire or real- analytic functions of their own signature, i.e. of iterated integrals of the process with itself, and allow therefore for a generic path dependence. We show that their pro- longation with the corresponding signature is an affine and polynomial process taking values in subsets of group-like elements of the extended tensor algebra. By relying on the duality theory for affine and polynomial processes we obtain explicit formulas in terms of novel and proper notions of converging power series for the Fourier-Laplace transform and the expected value of entire functions of the signature process. The coefficients of these power series are solutions of extended tensor algebra valued Ric- cati and linear ordinary differential equations (ODEs), respectively, whose vector fields can be expressed in terms of the entire characteristics of the corresponding SDEs. In other words, we construct a class of stochastic processes, which is universal within Itˆo processes with path-dependent characteristics and which allows for a relatively explicit characterization of the Fourier-Laplace transform and hence the full law on path space. We also analyze the special case of one-dimensional signature SDEs, which correspond to classical SDEs with real-analytic characteristics. Finally, the practical feasibility of this affine and polynomial approach is illustrated by several numerical examples
Josef Formánek prose write (talented, admired, cursed)
No full textThis thesis aims to introduce a new figure in Czech prose, Josef Formanek. The focus is predominantly on the interpretation and evaluation of the novel Mluviti pravdu. Other parts of the thesis deal with a comprehensive characterisation of individual works of the author. The outcome is to depict how Josef Formanek is placed in the context of contemporary Czech literature. The aim of the thesis is to provide a monography about the new author of Czech prose ,whose monography hasn't been written up as of yet
Selected topics in numerics of stochastic differential equations
No full textDie Vorliegende Arbeit beschäftigt sich mit einer Reihe von Fragen der Numerik stochastischer Differentialgleichungen bzw. mit numerischen Verfahren, welche auf stochastische Methoden beruhen. In allen behandelten Problemen werden geometrische Überlegungen und Verfahren ausgiebig verwendet.Nach einer Einleitung befasst sich Kapitel 2 mit der Geometrie der iterierten Integrale der Brown'schen Bewegung. Als Anwendung dieser Theorie wird das Kubaturverfahren am Wiener Raum von Terry Lyons und Nicolas Victoir präsentiert. Ferner stellen wir eine explizite Formel zur Berechnung der Momente der iterierten Integrale vor. In Kapitel 3 wird das Kubaturverfahren am Wienerraum für stochastische partielle Differentialgleichungen verallgemeinert, also für stochastische Differentialgleichungen auf unendlich dimensionalen Räumen.In Kapitel 4 stellen wir zwei neue Verfahren zur schwachen Approximation reflektierter Diffusionen, also Lösungen stochastischer Differentialgleichungen, die am Rand eines Gebietes reflektiert werden.Reflektierte Diffusionen sind von großer praktischer Bedeutung, weil sie die stochastische Repräsentation der Neumann Randwertprobleme der zugehörigen Wärmeleitungsgleichung ermöglichen. Der erste Algorithmus basiert auf die Hinzunahme eines Korrekturterms zum üblichen Euler-Maruyama Ansatz, während der zweite Algorithmus Adaptivität verwendet. Die Schlußfolgerungen werden durch numerische Beispiele untermauert.Im letzten Kapitel wird die Implementierung eines neuen Ansatzes des "Simuliertes Annealing"-Verfahrens vorgestellt. Das besondere dieses Ansatzes von Baudoin, Hairer und Teichmann liegt darin das hypo-elliptische, nicht notwendigerweise elliptische Prozesse verwendet werden können. Die besonderen numerischen Aspekte werden diskutiert und numerische Beispiele präsentiert.The present thesis is concerned with several Problems related to numerics of stochastic differential equations and to general numerical tasks, for which stochastic approaches can be used. In all these problems are analyzed withe their respective geometry in mind, and, moreover, geometric methods are used throughout the thesis.After a short introduction, Chapter 2 of the thesis starts with a discussion of the geometry of the iterated integrals of the Brownian motion. As an application of this theory, we present the method of cubature on Wiener space by Terry Lyons and Nicolas Victoir for weak approximation of stochastic differential equations. In the remainder of the chapter, an explicit formula for the moments of the iterated integrals and a algorithm for the computation of the moments of the corresponding Levy areas are presented. In Chapter 3, the cubature on Wiener space method is generalized to stochastic partial differential equations, i. e. to stochastic differential equations on an infinite dimensional space. In Chapter 4, we present two new algorithms for weak approximation of reflected diffusions. These are of special importance in the applications, because they allow for the stochastic representation of Neumann boundary value problems for the corresponding parabolic partial differential equations. The first algorithm is based on the addition of a correction term found by careful analysis of the error expansion of the well-known Euler-Maruyama scheme for reflected diffusions. The second algorithm is an adaptive one, using a local error density, again derived from the error expansion of the Euler scheme. These two schemes yield better orders of convergence than the Euler scheme, and are applicable in more general situations than the previous higher order schemes. These conclusions are backed up by numerical examples.In the last chapter, an implementation of a new simulated annealing method for global optimization of non-convex functions is presented. The new method was recently proposed by Baudoin, Hairer and Teichmann and consists of a horizontal gradient flow, which is perturbed by a hypo-elliptic process, and works on general homogenous spaces of nilpotent Lie groups. The method is tested in two numerical examples and its special numerical aspects are discussed
Interpretation of fairy tales authored by Josef Štefan Kubín
No full textInterpretation of fairy tales authored by Josef Štefan Kubín Ondřej Vojtíšek Abstract: This bachelor's thesis deals with interpretation of Josef Štefan Kubín's author fairy tales both in theory and application. Its goal is to describe options of interpretation of children's literature and to demonstrate these options by means of Kubín's literal work. As a result, this bachelor's thesis also highlights semantics riches and valuable qualities of this part of Kubín's work, which is being neglected by publishers nowadays. In its theoretical part, the thesis addresses several issues: different ways of interpretation of fairy tales, specification of the term "author fairy tale" and the different forms of Kubín's fairy tales. As a method of interpretation, synthesis of several approaches (Franz, Šmahelová, Urbanová, and others) was used and each of these approaches was described by one example. This synthesis provides insight into the meaning of fairy tales that can be therefore understood as representation of situations outlined not only with help of motives but with help of specific expressions as well. Collections of fairy tales authored by Kubín are analyzed in respect to the amount of Kubín's own invention compared with the quantity of folk motives. This analysis is accompanied by brief Kubín's biography and..
Markovian lifts of positive semidefinite affine Volterra-type processes
No full textWe consider stochastic partial differential equations appearing as Markovian lifts of matrix-valued (affine) Volterra-type processes from the point of view of the generalized Feller property (see, e.g., Dörsek and Teichmann in A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651). We introduce in particular Volterra Wishart processes with fractional kernels and values in the cone of positive semidefinite matrices. They are constructed from matrix products of infinite dimensional Ornstein–Uhlenbeck processes whose state space is the set of matrix-valued measures. Parallel to that we also consider positive definite Volterra pure jump processes, giving rise to multivariate Hawkes-type processes. We apply these affine covariance processes for multivariate (rough) volatility modeling and introduce a (rough) multivariate Volterra Heston-type model
Josef Mitterer’s Escape from Essentialism
No full textEwa Bińczyk Josef Mitterer’s Escape from Essentialism
In her review of Josef Mitterer’s book “Ucieczka z dowolności”, the Author provides a critical evaluation of the book which proposes to depart from dualist assumptions in the process of communication.Ewa Bińczyk Josef Mitterer’s Escape from Essentialism
In her review of Josef Mitterer’s book “Ucieczka z dowolności”, the Author provides a critical evaluation of the book which proposes to depart from dualist assumptions in the process of communication
Josef Willomitzer (1849 - 1900). Life and Work of German Writing Author from Bohemia.
No full textJosef Willomitzer (1849 - 1900). Life and Work of German Writing Author from Bohemia. The bachelor theses deals with life and work of german writing author from Bohemia, Josef Willomitzer. The work describes as a introduction the social and culture situation in Prague in the end of 19. century. The following chapters concern Willomitzers life and work in context of the historical and political development of Bohemia. The work is based on information available from ressources such as lexicons, newspaper articles and archive ressources. Apart from his life is in this work described also his journalistic activity. In the last part is summarized Willomitzers literary work. The analysis of chosen works which correspond to certain historical topics is also involved. The purpose of this work is to draw up a compact biography of Josef Willomitzer and a summary of his work. Keywords: Josef Willomitzer, humoresque, journalism, Bohemia, German Prague in the end of 19. centur
Josef Willomitzer (1849 - 1900). Life and Work of German Writing Author from Bohemia.
No full textJosef Willomitzer (1849 - 1900). Life and Work of German Writing Author from Bohemia. The bachelor theses deals with life and work of german writing author from Bohemia, Josef Willomitzer. The work describes as a introduction the social and culture situation in Prague in the end of 19. century. The following chapters concern Willomitzers life and work in context of the historical and political development of Bohemia. The work is based on information available from ressources such as lexicons, newspaper articles and archive ressources. Apart from his life is in this work described also his journalistic activity. In the last part is summarized Willomitzers literary work. The analysis of chosen works which correspond to certain historical topics is also involved. The purpose of this work is to draw up a compact biography of Josef Willomitzer and a summary of his work. Keywords: Josef Willomitzer, humoresque, journalism, Bohemia, German Prague in the end of 19. centur
- …
