Probability on Graphs
- 278 Seiten
- 10 Lesestunden
A user-friendly introduction for mathematicians to some of the principal stochastic models near the interface of probability and physics.
Lehrbücher des Instituts für Mathematische Statistik Reihe
Diese Reihe bietet prägnante Einführungen in aktuelle Themen der mathematischen Statistik. Konzipiert für fortgeschrittene Masterstudiengänge, Doktoranden und zum Selbststudium, bietet jeder Band einen fokussierten und doch umfassenden Überblick. Die Bücher sind in der Regel kürzer als herkömmliche Lehrbücher und basieren oft auf Material, das für spezifische Kurse entwickelt wurde. Mit Übungen ausgestattet, sind diese Bände ideal, um ein solides Verständnis moderner statistischer Konzepte zu erlangen.
Empfohlene Lesereihenfolge
This textbook offers a compact introduction to Malliavin calculus. It covers recent applications, and includes a self-contained presentation of preliminary material on Brownian motion and stochastic calculus. Accessible to non- experts, graduate students and researchers can use this book to master the core techniques necessary for further study.
IMS Textbooks - 10: Applied Stochastic Differential Equations
- 326 Seiten
- 12 Lesestunden
Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of It� calculus, the central theorems in the field, and such approximation schemes as stochastic Runge-Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-driven derivations and computational assignments. MATLAB/Octave source code is available for download, promoting hands-on work with the methods.
This account of the new and exciting area of noise sensitivity of Boolean functions - in particular applied to critical percolation - is designed for graduate students and researchers in probability theory, discrete mathematics, and theoretical computer science. It assumes a basic background in probability theory and integration theory. Each chapter ends with exercises.
The Surprising Mathematics of Longest Increasing Subsequences
- 366 Seiten
- 13 Lesestunden
Exploring the longest increasing subsequence problem reveals its intriguing connections to diverse mathematical fields, including random permutations and matrices. This book offers a playful yet detailed examination of these links, making complex concepts accessible to graduate students in mathematics, computer science, physics, and statistics. Key topics include the Vershik-Kerov-Logan-Shepp theorem, the Baik-Deift-Johansson theorem, and the Tracy-Widom distribution, showcasing significant advances in probability and combinatorics over the past four decades.
Communication networks underpin our modern world, and provide fascinating and challenging examples of large-scale stochastic systems. This compact introduction to some of the stochastic models found useful in the study of communication networks is ideal for graduate students wishing to understand this important area of application.