Combinatorial Stochastic Processes

Combinatorial Stochastic Processes

Coherent random allocations and the Ewens-Pitman formula. PDMI Preprint, Steklov Math. Institute, St. Petersburg, 1995. S. Kerov. The boundary of Young lattice and random Young tableaux. In Formal power series and algebraic ...

Author: Jim Pitman

Publisher: Springer Science & Business Media

ISBN: 9783540309901

Category: Mathematics

Page: 260

View: 526

The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.
Categories: Mathematics

Semiclassical Analysis for Diffusions and Stochastic Processes

Semiclassical Analysis for Diffusions and Stochastic Processes

Analytic solutions to some linear PDE In this short Section we collect some general facts on analytic (or even formal power series) solutions to linear first order partial differential equations of the form 6S XS + (4.

Author: Vassili N. Kolokoltsov

Publisher: Springer

ISBN: 9783540465874

Category: Mathematics

Page: 356

View: 149

The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Lévy processes, (iii) complex stochastic Schrödinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus.
Categories: Mathematics

Stochastic Processes Physics and Geometry New Interplays II

Stochastic Processes  Physics and Geometry  New Interplays  II

... on the linear space C TM ( M ) [ [ H ] ] of formal power series in ħ with coefficients in C® ( M ) . That means , in the language of formal deformation theory , one understands quantization as deformation of the Poisson - algebra C® ...

Author: Sergio Albeverio

Publisher: American Mathematical Soc.

ISBN: 0821819607

Category: Mathematics

Page: 333

View: 374

This volume and Stochastic Processes, Physics and Geometry: New Interplays. I present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, ``Infinite Dimensional (Stochastic) Analysis and Quantum Physics'', was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers.
Categories: Mathematics

Stochastic Processes Physics And Geometry Ii Proceedings Of The Iii International Conference

Stochastic Processes  Physics And Geometry Ii   Proceedings Of The Iii International Conference

The scheme has been used to attack a series of stochastic partial differential equations. We will here as an example study the equation Au ... H.,(w) e L*(u), then F(z) = ?ts(z) = XC c.2° (39) as a formal power series in z = (21, ...).

Author: Albeverio Sergio

Publisher: World Scientific

ISBN: 9789814549691

Category:

Page: 756

View: 829

In the last few years there has been an explosion of activity in the field of the dynamics of fractal surfaces, which, through the convergence of important new results from computer simulations, analytical theories and experiments, has led to significant advances in our understanding of nonequilibrium surface growth phenomena. This interest in surface growth phenomena has been motivated largely by the fact that a wide variety of natural and industrial processes lead to the formation of rough surfaces and interfaces. This book presents these developments in a single volume by bringing together the works containing the most important results in the field.The material is divided into chapters consisting of reprints related to a single major topic. Each chapter has a general introduction to a particular aspect of growing fractal surfaces. These introductory parts are included in order to provide a scientific background to the papers reproduced in the main part of the chapters. They are written in a pedagogical style and contain only the most essential information. The contents of the reprints are made more accessible to the reader as they are preceded by a short description of what the editors find to be the most significant results in the paper.
Categories:

Modelling and Application of Stochastic Processes

Modelling and Application of Stochastic Processes

A. 277 ( 2 mo g(z) q' (z) and we may extend this definition by linearity to multiplication of g (2) by any power series f(z), at least formally. Notice that we have a unique additive decomposition: zg (z) = 2 * g (2) + g' (z) where the ...

Author: Uday B. Desai

Publisher: Springer Science & Business Media

ISBN: 9781461322672

Category: Science

Page: 288

View: 317

The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side, chapters on use of Markov random fields for modelling and analyzing image signals, use of complementary models for the smoothing problem with missing data, and nonlinear estimation are included. Chapter 1 by Klein and Dickinson develops the nested orthogonal state space realization for ARMA processes. As suggested by the name, nested orthogonal realizations possess two key properties; (i) the state variables are orthogonal, and (ii) the system matrices for the (n + l)st order realization contain as their "upper" n-th order blocks the system matrices from the n-th order realization (nesting property).
Categories: Science

Stochastic Processes and their Applications

Stochastic Processes and their Applications

In applications it may happen that the expectations of the random operators under consideration all commute. ... Since the GNS representation it cannot be used, we employ formal power series as in Section 2 of Ref. 1, X 4 a. X ... a.

Author: Sergio Albeverio

Publisher: Springer Science & Business Media

ISBN: 9789400921177

Category: Mathematics

Page: 403

View: 560

'Et moi ..., si j'avait su comment en revenIT, One service mathematics has rendered the je n'y serais point allt\.' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. :; 'One service logic has rendered com puter science .. :; 'One service category theory has rendered mathematics .. :. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Categories: Mathematics

Stochastic Processes and Random Matrices

Stochastic Processes and Random Matrices

Continuing this process with A3, ..., AN, we obtain for any 6 × 0 and N > 1: R. v. " k; (Al...AN) = YE ** IIT,(A)(A, ... Alternatively, it is enough to think that we are working with formal power series. Fig. 2.26 A possible choice of ...

Author: Grégory Schehr

Publisher: Oxford University Press

ISBN: 9780198797319

Category: Mathematics

Page: 672

View: 593

The field of stochastic processes and Random Matrix Theory (RMT) has been a rapidly evolving subject during the last fifteen years. The continuous development and discovery of new tools, connections and ideas have led to an avalanche of new results. These breakthroughs have been made possible thanks, to a large extent, to the recent development of various new techniques in RMT. Matrix models have been playing an important role in theoretical physics for a long time and they are currently also a very active domain of research in mathematics. An emblematic example of these recent advances concerns the theory of growth phenomena in the Kardar-Parisi-Zhang (KPZ) universality class where the joint efforts of physicists and mathematicians during the last twenty years have unveiled the beautiful connections between this fundamental problem of statistical mechanics and the theory of random matrices, namely the fluctuations of the largest eigenvalue of certain ensembles of random matrices. This text not only covers this topic in detail but also presents more recent developments that have emerged from these discoveries, for instance in the context of low dimensional heat transport (on the physics side) or integrable probability (on the mathematical side).
Categories: Mathematics

High dimensional Nonlinear Diffusion Stochastic Processes

High dimensional Nonlinear Diffusion Stochastic Processes

as the solution of problem ( 1.12.16 ) , ( 1.5.7 ) in the form of formal power series with respect to A ( see ( 5 ) in Roy and Spanos , 1993 ) . In so doing , the rigorous mathematical justification is not attempted ( see the text just ...

Author: Yevgeny Mamontov

Publisher: World Scientific

ISBN: 9812810544

Category: Mathematics

Page: 324

View: 369

Annotation This book is one of the first few devoted to high-dimensional diffusion stochastic processes with nonlinear coefficients. These processes are closely associated with large systems of Ito's stochastic differential equations and with discretized-in-the-parameter versions of Ito's stochastic differential equations that are nonlocally dependent on the parameter. The latter models include Ito's stochastic integro-differential, partial differential and partial integro-differential equations.The book presents the new analytical treatment which can serve as the basis of a combined, analytical -- numerical approach to greater computational efficiency. Some examples of the modelling of noise in semiconductor devices are provided
Categories: Mathematics

Linear Stochastic Systems

Linear Stochastic Systems

(5) The process u has a representation of the form OO u = Y, Eug-i + we ke Z, i = 1 where w is full rank and wel H_1 ... on a wide-sense stationary process u, the formal power-series multiplication Z(z)u(z) yields a formal power series ...

Author: Peter E. Caines

Publisher: SIAM

ISBN: 9781611974713

Category: Mathematics

Page: 874

View: 755

Linear Stochastic Systems, originally published in 1988, is today as comprehensive a reference to the theory of linear discrete-time-parameter systems as ever. Its most outstanding feature is the unified presentation, including both input-output and state space representations of stochastic linear systems, together with their interrelationships. The author first covers the foundations of linear stochastic systems and then continues through to more sophisticated topics including the fundamentals of stochastic processes and the construction of stochastic systems; an integrated exposition of the theories of prediction, realization (modeling), parameter estimation, and control; and a presentation of stochastic adaptive control theory. Written in a clear, concise manner and accessible to graduate students, researchers, and teachers, this classic volume also includes background material to make it self-contained and has complete proofs for all the principal results of the book. Furthermore, this edition includes many corrections of errata collected over the years.
Categories: Mathematics

Advances in Inequalities for Series

Advances in Inequalities for Series

Theorem 1.3 may be useful where generating functions or formal power series are utilized such as in enumerative combinatorics and stochastic processes ( cf. Wilf [ 48 ] , Feller [ 22 ] , Kijima [ 26 ] , Heathcote ( 24 ] , Kendall [ 25 ] ...

Author: Sever Silvestru Dragomir

Publisher: Nova Publishers

ISBN: 1600219209

Category: Mathematics

Page: 233

View: 865

This research monograph, deals with identities and inequalities relating to series and their application. This is the first volume of research monographs on advances in inequalities for series. All of the papers in this volume have been fully peer reviewed. Some papers in this volume appear in print for the first time, detailing many technical results and some other papers offer a review of a number of recently published results. The papers appear in author alphabetical order and not in mathematics subject classification. There are fifteen diverse papers in this volume each with its own speciality. An important issue in many applications of Probability Theory is finding an approximate measure of distance, or discrimination, between two probability distributions. A number of divergence measures for this purpose have been proposed.
Categories: Mathematics