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  • Asymptotic Analysis for Functional Stochastic Differential Equations

    Series series Mathematics and Statistics (R0)
    This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, ... Read more

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    Modeling Aspects of Urban Life

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  • Approximation Methods in Probability Theory

    Series series Mathematics and Statistics (R0)
    This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook ... Read more

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    Series Book 72 - Probability Theory and Stochastic Modelling
    This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems.First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the ... Read more

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  • From Particle Systems to Partial Differential Equations

    PSPDE IV, Braga, Portugal, December 2015

    Series series Springer Nature Proceedings excluding Computer Science
    "This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic “basic” terms involved in the formulation of the dynamic Ö4 theory in three space dimensions, as well as selected contributions presented at ... Read more

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  • Brownian Motion and its Applications to Mathematical Analysis

    École d'Été de Probabilités de Saint-Flour XLIII – 2013

    Series series Mathematics and Statistics (R0)
    These lecture notes provide an introduction to the applications of Brownian motion to analysis and more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical ... Read more

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  • Operator Inequalities of the Jensen, Čebyšev and Grüss Type

    Series series Mathematics and Statistics (R0)
    The main aim of this bookis to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces.In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The generalized Schwarz’s inequality for positive selfadjoint ... Read more

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  • Brownian Dynamics at Boundaries and Interfaces

    In Physics, Chemistry, and Biology

    by Zeev Schuss ...
    Series series Mathematics and Statistics (R0)
    Brownian dynamics serve as mathematical models for the diffusive motion of microscopic particles of various shapes in gaseous, liquid, or solid environments. The renewed interest in Brownian dynamics is due primarily to their key role in molecular and cellular biophysics: diffusion of ions and molecules is the driver of all life. Brownian dynamics simulations are the numerical realizations of ... Read more

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    Particle Systems and PDEs, Braga, Portugal, December 2012

    Series series Springer Nature Proceedings excluding Computer Science
    This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I, which took place at the Centre of Mathematics of the University of Minho, Braga, Portugal, from the 5th to the 7th of December, 2012.The purpose of the conference was to bring together world leaders to discuss their topics of expertise and to present some of their latest ... Read more

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    Series Book 12 - SpringerBriefs in Mathematical Physics
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    Waves in Neural Media: From Single Neurons to Neural Fields surveys mathematical models of traveling waves in the brain, ranging from intracellular waves in single neurons to waves of activity in large-scale brain networks. The work provides a pedagogical account of analytical methods for finding traveling wave solutions of the variety of nonlinear differential equations that arise in such models. ... Read more

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  • Probability

    The Classical Limit Theorems

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    Probability theory has been extraordinarily successful at describing a variety of phenomena, from the behaviour of gases to the transmission of messages, and is, besides, a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bell-shaped curve, the law of averages, and so on, concepts that crop up in so many ... Read more

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