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Random Walk A Modern Introduction

Author: Gregory F. Lawler
Publisher: Cambridge University Press
ISBN: 1139488767
Size: 49.64 MB
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Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.

Non Homogeneous Random Walks

Author: Mikhail Menshikov
Publisher: Cambridge University Press
ISBN: 1316867366
Size: 25.10 MB
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Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems.

Intersection Local Times Loop Soups And Permanental Wick Powers

Author: Yves Le Jan
Publisher: American Mathematical Soc.
ISBN: 1470436957
Size: 47.45 MB
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Several stochastic processes related to transient Lévy processes with potential densities , that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures endowed with a metric . Sufficient conditions are obtained for the continuity of these processes on . The processes include -fold self-intersection local times of transient Lévy processes and permanental chaoses, which are `loop soup -fold self-intersection local times' constructed from the loop soup of the Lévy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of -th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above.

Algorithms And Computation

Author: Khaled Elbassioni
Publisher: Springer
ISBN: 3662489716
Size: 50.75 MB
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This book constitutes the refereed proceedings of the 26th International Symposium on Algorithms and Computation, ISAAC 2015, held in Nagoya, Japan, in December 2015. The 65 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 180 submissions for inclusion in the book. The focus of the volume is on the following topics: computational geometry; data structures; combinatorial optimization and approximation algorithms; randomized algorithms; graph algorithms and FPT; computational complexity; graph drawing and planar graphs; online and streaming algorithms; and string and DNA algorithms.

Probability And Statistical Physics In St Petersburg

Author: V. Sidoravicius
Publisher: American Mathematical Soc.
ISBN: 1470422484
Size: 48.96 MB
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This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.

Geometric Analysis

Author: Peter Li
Publisher: Cambridge University Press
ISBN: 1107020646
Size: 66.86 MB
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Basic techniques for researchers interested in the field of geometric analysis.

Probability On Graphs

Author: Geoffrey Grimmett
Publisher: Cambridge University Press
ISBN: 1108438172
Size: 48.82 MB
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A user-friendly introduction for mathematicians to some of the principal stochastic models near the interface of probability and physics.

Financial Derivatives

Author: Jamil Baz
Publisher: Cambridge University Press
ISBN: 9780521815109
Size: 23.58 MB
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This book offers a complete, succinct account of the principles of financial derivatives pricing. The first chapter provides readers with an intuitive exposition of basic random calculus. Concepts such as volatility and time, random walks, geometric Brownian motion, and Ito's lemma are discussed heuristically. The second chapter develops generic pricing techniques for assets and derivatives, determining the notion of a stochastic discount factor or pricing kernel, and then uses this concept to price conventional and exotic derivatives. The third chapter applies the pricing concepts to the special case of interest rate markets, namely, bonds and swaps, and discusses factor models and term structure consistent models. The fourth chapter deals with a variety of mathematical topics that underlie derivatives pricing and portfolio allocation decisions such as mean-reverting processes and jump processes and discusses related tools of stochastic calculus such as Kolmogorov equations, martingale techniques, stochastic control, and partial differential equations.

Probability

Author: Geoffrey Grimmett
Publisher: Oxford University Press
ISBN: 019870996X
Size: 11.51 MB
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Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains.Three specialfeatures of this book are its modest size, the fairly broad range of topics covered, and its approach to mathematical rigour: not everything is rigorous, but the need for rigour is explained wherenecessary.This second edition develops the success of the first edition through an updated presentation, an extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.