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Asymptotic Methods in Probability and Statistics
  • Language: en
  • Pages: 925

Asymptotic Methods in Probability and Statistics

  • Type: Book
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  • Published: 1998-10-29
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  • Publisher: Elsevier

One of the aims of the conference on which this book is based, was to provide a platform for the exchange of recent findings and new ideas inspired by the so-called Hungarian construction and other approximate methodologies. This volume of 55 papers is dedicated to Miklós Csörgő a co-founder of the Hungarian construction school by the invited speakers and contributors to ICAMPS'97.This excellent treatize reflects the many developments in this field, while pointing to new directions to be explored. An unequalled contribution to research in probability and statistics.

Topics in Spatial Stochastic Processes
  • Language: en
  • Pages: 268

Topics in Spatial Stochastic Processes

The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.

Point Processes and Their Statistical Inference
  • Language: en
  • Pages: 524

Point Processes and Their Statistical Inference

  • Type: Book
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  • Published: 2017-09-06
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  • Publisher: Routledge

First Published in 2017. Routledge is an imprint of Taylor & Francis, an Informa company.

Simplicial Complexes of Graphs
  • Language: en
  • Pages: 376

Simplicial Complexes of Graphs

  • Type: Book
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  • Published: 2007-12-10
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  • Publisher: Springer

A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.

From Hahn-Banach to Monotonicity
  • Language: en
  • Pages: 251

From Hahn-Banach to Monotonicity

This new edition of LNM 1693 aims to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a "big convexification" of the graph of the multifunction and the "minimax technique" for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with the Hahn-Banach theorem and culminates in a survey of current results on monotone multifunctions on a Banach space.

Evolution Algebras and Their Applications
  • Language: en
  • Pages: 136

Evolution Algebras and Their Applications

Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.

Parameter Estimation in Stochastic Differential Equations
  • Language: en
  • Pages: 271

Parameter Estimation in Stochastic Differential Equations

  • Type: Book
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  • Published: 2007-09-26
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  • Publisher: Springer

Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

Weighted Littlewood-Paley Theory and Exponential-Square Integrability
  • Language: en
  • Pages: 233

Weighted Littlewood-Paley Theory and Exponential-Square Integrability

  • Type: Book
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  • Published: 2007-12-31
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  • Publisher: Springer

Littlewood-Paley theory extends some of the benefits of orthogonality to situations where it doesn’t make sense by letting certain oscillatory infinite series of functions be controlled in terms of infinite series of non-negative functions. Beginning in the 1980s, it was discovered that this control could be made much sharper. This book offers a gentle, well-motivated introduction to those discoveries, the methods behind them, their consequences, and some of their applications.

Transseries and Real Differential Algebra
  • Language: en
  • Pages: 265

Transseries and Real Differential Algebra

  • Type: Book
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  • Published: 2006-10-31
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  • Publisher: Springer

Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.