Weak approximations. A Malliavin calculus approach

We introduce a variation of the proof for weak approximations that issuitable for studying the densities of stochastic processes which areevaluations of the flow generated by a stochastic differential equation on a random variable that maybe anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore if the inverse of the Malliavin covariance matrix associated with the process under consideration is sufficiently integrable then approximations fordensities and distributions can also be achieved. We apply theseideas to the case of stochastic differential equations with boundaryconditions and the composition of two diffusions.

Large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order

The spectral theory for linear autonomous neutral functional differential equations (FDE) yields explicit formulas for the large time behaviour of solutions. Our results are based on resolvent computations and Dunford calculus, applied to establish explicit formulas for the large time behaviour of solutions of FDE. We investigate in detail a class of two-dimensional systems of FDE. (C) 2009 Elsevier Inc. All rights reserved.

About the minimum time transference in a fractional differential equation

The use of fractional calculus when modeling phenomena allows new queries concerning the deepest parts of the physical laws involved in. Here we will be dealing with an apparent paradox in which the time of transference from zero in a system with fractional derivatives can be strictly shortened relatively to the minimal time transference done in an equivalent system in the frame of the entire derivatives.

The Devil’s Calculus: Mathematical Models of Civil War

In spite of the movement to turn political science into a real science, various mathematical methods that are now the staples of physics, biology, and even economics are thoroughly uncommon in political science, especially the study of civil war. This study seeks to apply such methods - specifically, ordinary differential equations (ODEs) - to model civil war based on what one might dub the capabilities school of thought, which roughly states that civil wars end only when one side’s ability to make war falls far enough to make peace truly attractive. I construct several different ODE-based models and then test them all to see which best predicts the instantaneous capabilities of both sides of the Sri Lankan civil war in the period from 1990 to 1994 given parameters and initial conditions. The model that the tests declare most accurate gives very accurate predictions of state military capabilities and reasonable short term predictions of cumulative deaths. Analysis of the model reveals the scale of the importance of rebel finances to the sustainability of insurgency, most notably that the number of troops required to put down the Tamil Tigers is reduced by nearly a full order of magnitude when Tiger foreign funding is stopped. The study thus demonstrates that accurate foresight may come of relatively simple dynamical models, and implies the great potential of advanced and currently unconventional non-statistical mathematical methods in political science.

Introduction to the calculus,

"A revision of the author's A first course in the differential and integral calculus."--Pref.

Introduction to the calculus,

"A revision of the author's A first course in the differential and integral calculus."--Pref.

Calculus, with analytic geometry.

Includes index.

Lehrbuch der Differential- und Integralrechnung;

Vol. 1: 2d ed., 1897; vol. 2; 1st ed., 1885; vol. 3: 2d ed., 1904.

Anwendung der Differential- und Integralrechnung auf Geometrie: eine Revision der Principien. Vorlesung gehalten während des Sommersemesters 1901,

Available on demand as hard copy or computer file from Cornell University Library.

Vorlesungen über die elemente der differential- und integralrechnung und ihre anwendung zur beschreibung von naturerscheinungen

Available on demand as hard copy or computer file from Cornell University Library.

Hauptsätze der Differential- und Integral-Rechnung, als Leitfaden zum Gebrauch bei Vorlesungen.

Available on demand as hard copy or computer file from Cornell University Library.

Grundzüge der differential- und integralrechnung.

Available on demand as hard copy or computer file from Cornell University Library.

Die Elemente der Differential- und Integralrechnung. Zur Einführung in das Studium,

Available on demand as hard copy or computer file from Cornell University Library.

Differential- und integralrechnung ...

Available on demand as hard copy or computer file from Cornell University Library.

Övningsuppgifter i differential-kalkyl och algebraisk analys ...

Mode of access: Internet.