Dirichlet Forms Methods For Poisson Point Measures And Lévy Processes

Dirichlet Forms Methods For Poisson Point Measures And Lévy Processes Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Dirichlet Forms Methods For Poisson Point Measures And Lévy Processes book. This book definitely worth reading, it is an incredibly well-written.

Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes

Nicolas Bouleau,Laurent Denis
Dirichlet Forms Methods for Poisson Point Measures and L vy Processes Book PDF

Author : Nicolas Bouleau,Laurent Denis
Publisher : Springer
Page : 323 pages
File Size : 54,6 Mb
Release : 2016-01-08
Category : Mathematics
ISBN : 9783319258201

Get Book

Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes by Nicolas Bouleau,Laurent Denis Pdf

A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the “lent particle method” it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson functionals. The method gives rise to a new explicit calculus that they illustrate on various examples: it consists in adding a particle and then removing it after computing the gradient. Using this method, one can establish absolute continuity of Poisson functionals such as Lévy areas, solutions of SDEs driven by Poisson measure and, by iteration, obtain regularity of laws. The authors also give applications to error calculus theory. This book will be of interest to researchers and graduate students in the fields of stochastic analysis and finance, and in the domain of statistical physics. Professors preparing courses on these topics will also find it useful. The prerequisite is a knowledge of probability theory.

Poisson Point Processes and Their Application to Markov Processes

Kiyosi Itô
Poisson Point Processes and Their Application to Markov Processes Book PDF

Author : Kiyosi Itô
Publisher : Springer
Page : 43 pages
File Size : 52,9 Mb
Release : 2015-12-24
Category : Mathematics
ISBN : 9789811002724

Get Book

Poisson Point Processes and Their Application to Markov Processes by Kiyosi Itô Pdf

An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {a} (called the jumping-in measure and a non-negative number m

The Mathematics of Errors

Nicolas Bouleau
The Mathematics of Errors Book PDF

Author : Nicolas Bouleau
Publisher : Springer Nature
Page : 448 pages
File Size : 54,6 Mb
Release : 2022-03-27
Category : Mathematics
ISBN : 9783030885755

Get Book

The Mathematics of Errors by Nicolas Bouleau Pdf

The Mathematics of Errors presents an original, rigorous and systematic approach to the calculus of errors, targeted at both the engineer and the mathematician. Starting from Gauss's original point of view, the book begins as an introduction suitable for graduate students, leading to recent developments in stochastic analysis and Malliavin calculus, including contributions by the author. Later chapters, aimed at a more mature audience, require some familiarity with stochastic calculus and Dirichlet forms. Sensitivity analysis, in particular, plays an important role in the book. Detailed applications in a range of fields, such as engineering, robotics, statistics, financial mathematics, climate science, or quantum mechanics are discussed through concrete examples. Throughout the book, error analysis is presented in a progressive manner, motivated by examples and appealing to the reader’s intuition. By formalizing the intuitive concept of error and richly illustrating its scope for application, this book provides readers with a blueprint to apply advanced mathematics in practical settings. As such, it will be of immediate interest to engineers and scientists, whilst providing mathematicians with an original presentation. Nicolas Bouleau has directed the mathematics center of the Ecole des Ponts ParisTech for more than ten years. He is known for his theory of error propagation in complex models. After a degree in engineering and architecture, he decided to pursue a career in mathematics under the influence of Laurent Schwartz. He has also written on the production of knowledge, sustainable economics and mathematical models in finance. Nicolas Bouleau is a recipient of the Prix Montyon from the French Academy of Sciences.

Séminaire de Probabilités XLIII

Catherine Donati Martin,Antoine Lejay,Alain Rouault
S minaire de Probabilit s XLIII Book PDF

Author : Catherine Donati Martin,Antoine Lejay,Alain Rouault
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 52,6 Mb
Release : 2010-10-28
Category : Mathematics
ISBN : 9783642152160

Get Book

Séminaire de Probabilités XLIII by Catherine Donati Martin,Antoine Lejay,Alain Rouault Pdf

This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.

Stochastic Calculus of Variations

Yasushi Ishikawa
Stochastic Calculus of Variations Book PDF

Author : Yasushi Ishikawa
Publisher : Walter de Gruyter GmbH & Co KG
Page : 376 pages
File Size : 42,9 Mb
Release : 2023-07-24
Category : Mathematics
ISBN : 9783110675290

Get Book

Stochastic Calculus of Variations by Yasushi Ishikawa Pdf

This book is a concise introduction to the stochastic calculus of variations for processes with jumps. The author provides many results on this topic in a self-contained way for e.g., stochastic differential equations (SDEs) with jumps. The book also contains some applications of the stochastic calculus for processes with jumps to the control theory, mathematical finance and so. This third and entirely revised edition of the work is updated to reflect the latest developments in the theory and some applications with graphics.

Stochastic Flows and Jump-Diffusions

Hiroshi Kunita
Stochastic Flows and Jump Diffusions Book PDF

Author : Hiroshi Kunita
Publisher : Springer
Page : 352 pages
File Size : 46,9 Mb
Release : 2019-03-26
Category : Mathematics
ISBN : 9789811338014

Get Book

Stochastic Flows and Jump-Diffusions by Hiroshi Kunita Pdf

This monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processes with jumps.In the first part of the book, it is shown that solutions of stochastic differential equations define stochastic flows of diffeomorphisms. Then, the relation between stochastic flows and heat equations is discussed. The latter part investigates fundamental solutions of these heat equations (heat kernels) through the study of the Malliavin calculus. The author obtains smooth densities for transition functions of various types of diffusions and jump-diffusions and shows that these density functions are fundamental solutions for various types of heat equations and backward heat equations. Thus, in this book fundamental solutions for heat equations and backward heat equations are constructed independently of the theory of partial differential equations.Researchers and graduate student in probability theory will find this book very useful.

Festschrift Masatoshi Fukushima

Zhen-Qing Chen,Niels Jacob,Masayoshi Takeda,Toshihiro Uemura
Festschrift Masatoshi Fukushima Book PDF

Author : Zhen-Qing Chen,Niels Jacob,Masayoshi Takeda,Toshihiro Uemura
Publisher : World Scientific
Page : 620 pages
File Size : 54,5 Mb
Release : 2014-11-27
Category : Mathematics
ISBN : 9789814596541

Get Book

Festschrift Masatoshi Fukushima by Zhen-Qing Chen,Niels Jacob,Masayoshi Takeda,Toshihiro Uemura Pdf

This book contains original research papers by leading experts in the fields of probability theory, stochastic analysis, potential theory and mathematical physics. There is also a historical account on Masatoshi Fukushima's contribution to mathematics, as well as authoritative surveys on the state of the art in the field. Contents:Professor Fukushima's Work:The Mathematical Work of Masatoshi Fukushima — An Essay (Zhen-Qing Chen, Niels Jacob, Masayoshi Takeda and Toshihiro Uemura)Bibliography of Masatoshi FukushimaContributions:Quasi Regular Dirichlet Forms and the Stochastic Quantization Problem (Sergio Albeverio, Zhi-Ming Ma and Michael Röckner)Comparison of Quenched and Annealed Invariance Principles for Random Conductance Model: Part II (Martin Barlow, Krzysztof Burdzy and Adám Timár)Some Historical Aspects of Error Calculus by Dirichlet Forms (Nicolas Bouleau)Stein's Method, Malliavin Calculus, Dirichlet Forms and the Fourth Moment Theorem (Louis H Y Chen and Guillaume Poly)Progress on Hardy-Type Inequalities (Mu-Fa Chen)Functional Inequalities for Pure-Jump Dirichlet Forms (Xin Chen, Feng-Yu Wang and Jian Wang)Additive Functionals and Push Forward Measures Under Veretennikov's Flow (Shizan Fang and Andrey Pilipenko)On a Result of D W Stroock (Patrick J Fitzsimmons)Consistent Risk Measures and a Non-Linear Extension of Backwards Martingale Convergence (Hans Föllmer and Irina Penner)Unavoidable Collections of Balls for Processes with Isotropic Unimodal Green Function (Wolfhard Hansen)Functions of Locally Bounded Variation on Wiener Spaces (Masanori Hino)A Dirichlet Space on Ends of Tree and Superposition of Nodewise Given Dirichlet Forms with Tier Linkage (Hiroshi Kaneko)Dirichlet Forms in Quantum Theory (Witold Karwowski and Ludwig Streit)On a Stability of Heat Kernel Estimates under Generalized Non-Local Feynman-Kac Perturbations for Stable-Like Processes (Daehong Kim and Kazuhiro Kuwae)Martin Boundary for Some Symmetric Lévy Processes (Panki Kim, Renming Song and Zoran Vondraček)Level Statistics of One-Dimensional Schrödinger Operators with Random Decaying Potential (Shinichi Kotani and Fumihiko Nakano)Perturbation of the Loop Measure (Yves Le Jan and Jay Rosen)Regular Subspaces of Dirichlet Forms (Liping Li and Jiangang Ying)Quasi-Regular Semi-Dirichlet Forms and Beyond (Zhi-Ming Ma, Wei Sun and Li-Fei Wang)Large Deviation Estimates for Controlled Semi-Martingales (Hideo Nagai)A Comparison Theorem for Backward SPDEs with Jumps (Bernt Øksendal, Agnès Sulem and Tusheng Zhang)On a Construction of a Space-Time Diffusion Process with Boundary Condition (Yoichi Oshima)Lower Bounded Semi-Dirichlet Forms Associated with Lévy Type Operators (René L Schilling and Jian Wang)Ultracontractivity for Non-Symmetric Markovian Semigroups (Ichiro Shigekawa)Metric Measure Spaces with Variable Ricci Bounds and Couplings of Brownian Motions (Karl-Theodor Sturm)Intrinsic Ultracontractivity and Semi-Small Perturbation for Skew Product Diffusion Operators (Matsuyo Tomisaki) Readership: Researchers in probability, stochastic analysis and mathematical physics. Key Features:Research papers by leading expertsHistorical account of M Fukushima's contribution to mathematicsAuthoritative surveys on the state of the art in the fieldKeywords:Probability Theory;Markov Processes;Dirichlet Forms;Potential Theory;Mathematical Physics

Jump SDEs and the Study of Their Densities

Arturo Kohatsu-Higa,Atsushi Takeuchi
Jump SDEs and the Study of Their Densities Book PDF

Author : Arturo Kohatsu-Higa,Atsushi Takeuchi
Publisher : Springer
Page : 355 pages
File Size : 43,7 Mb
Release : 2019-08-13
Category : Mathematics
ISBN : 9789813297418

Get Book

Jump SDEs and the Study of Their Densities by Arturo Kohatsu-Higa,Atsushi Takeuchi Pdf

The present book deals with a streamlined presentation of Lévy processes and their densities. It is directed at advanced undergraduates who have already completed a basic probability course. Poisson random variables, exponential random variables, and the introduction of Poisson processes are presented first, followed by the introduction of Poisson random measures in a simple case. With these tools the reader proceeds gradually to compound Poisson processes, finite variation Lévy processes and finally one-dimensional stable cases. This step-by-step progression guides the reader into the construction and study of the properties of general Lévy processes with no Brownian component. In particular, in each case the corresponding Poisson random measure, the corresponding stochastic integral, and the corresponding stochastic differential equations (SDEs) are provided. The second part of the book introduces the tools of the integration by parts formula for jump processes in basic settings and first gradually provides the integration by parts formula in finite-dimensional spaces and gives a formula in infinite dimensions. These are then applied to stochastic differential equations in order to determine the existence and some properties of their densities. As examples, instances of the calculations of the Greeks in financial models with jumps are shown. The final chapter is devoted to the Boltzmann equation.

Stochastic Analysis with Financial Applications

Arturo Kohatsu-Higa,Nicolas Privault,Shuenn-Jyi Sheu
Stochastic Analysis with Financial Applications Book PDF

Author : Arturo Kohatsu-Higa,Nicolas Privault,Shuenn-Jyi Sheu
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 49,7 Mb
Release : 2011-07-22
Category : Mathematics
ISBN : 9783034800976

Get Book

Stochastic Analysis with Financial Applications by Arturo Kohatsu-Higa,Nicolas Privault,Shuenn-Jyi Sheu Pdf

Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. The book also covers the areas of backward stochastic differential equations via the (non-linear) G-Brownian motion and the case of jump processes. Concerning the applications to finance, many of the articles deal with the valuation and hedging of credit risk in various forms, and include recent results on markets with transaction costs.

Hyperfinite Dirichlet Forms and Stochastic Processes

Sergio Albeverio,Ruzong Fan,Frederik S. Herzberg
Hyperfinite Dirichlet Forms and Stochastic Processes Book PDF

Author : Sergio Albeverio,Ruzong Fan,Frederik S. Herzberg
Publisher : Springer
Page : 284 pages
File Size : 54,9 Mb
Release : 2011-05-29
Category : Mathematics
ISBN : 3642196586

Get Book

Hyperfinite Dirichlet Forms and Stochastic Processes by Sergio Albeverio,Ruzong Fan,Frederik S. Herzberg Pdf

This monograph treats the theory of Dirichlet forms from a comprehensive point of view, using "nonstandard analysis." Thus, it is close in spirit to the discrete classical formulation of Dirichlet space theory by Beurling and Deny (1958). The discrete infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same methods. This setting has the advantage of being independent of special topological properties of the state space and in this sense is a natural one, valid for both finite- and infinite-dimensional spaces. The present monograph provides a thorough treatment of the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes, and summarizes in an epilogue the model-theoretic genericity of hyperfinite stochastic processes theory.

Fluctuation Theory for Lévy Processes

Ronald A. Doney
Fluctuation Theory for L vy Processes Book PDF

Author : Ronald A. Doney
Publisher : Springer
Page : 155 pages
File Size : 51,8 Mb
Release : 2007-04-25
Category : Mathematics
ISBN : 9783540485117

Get Book

Fluctuation Theory for Lévy Processes by Ronald A. Doney Pdf

Lévy processes, that is, processes in continuous time with stationary and independent increments, form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, and of course finance, where they include particularly important examples having "heavy tails." Their sample path behaviour poses a variety of challenging and fascinating problems, which are addressed in detail.

An Introduction to the Theory of Point Processes

D.J. Daley,D. Vere-Jones
An Introduction to the Theory of Point Processes Book PDF

Author : D.J. Daley,D. Vere-Jones
Publisher : Springer Science & Business Media
Page : 471 pages
File Size : 54,6 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387215648

Get Book

An Introduction to the Theory of Point Processes by D.J. Daley,D. Vere-Jones Pdf

Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.

Poisson Processes

J. F. C. Kingman
Poisson Processes Book PDF

Author : J. F. C. Kingman
Publisher : Clarendon Press
Page : 118 pages
File Size : 42,5 Mb
Release : 1992-12-17
Category : Mathematics
ISBN : 9780191591242

Get Book

Poisson Processes by J. F. C. Kingman Pdf

In the theory of random processes there are two that are fundamental, and occur over and over again, often in surprising ways. There is a real sense in which the deepest results are concerned with their interplay. One, the Bachelier Wiener model of Brownian motion, has been the subject of many books. The other, the Poisson process, seems at first sight humbler and less worthy of study in its own right. Nearly every book mentions it, but most hurry past to more general point processes or Markov chains. This comparative neglect is ill judged, and stems from a lack of perception of the real importance of the Poisson process. This distortion partly comes about from a restriction to one dimension, while the theory becomes more natural in more general context. This book attempts to redress the balance. It records Kingman's fascination with the beauty and wide applicability of Poisson processes in one or more dimensions. The mathematical theory is powerful, and a few key results often produce surprising consequences.

Lectures on the Poisson Process

Günter Last,Mathew Penrose
Lectures on the Poisson Process Book PDF

Author : Günter Last,Mathew Penrose
Publisher : Cambridge University Press
Page : 315 pages
File Size : 48,5 Mb
Release : 2017-10-26
Category : Mathematics
ISBN : 9781107088016

Get Book

Lectures on the Poisson Process by Günter Last,Mathew Penrose Pdf

A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

The Poisson-Dirichlet Distribution and Related Topics

Shui Feng
The Poisson Dirichlet Distribution and Related Topics Book PDF

Author : Shui Feng
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 44,7 Mb
Release : 2010-05-27
Category : Mathematics
ISBN : 9783642111945

Get Book

The Poisson-Dirichlet Distribution and Related Topics by Shui Feng Pdf

Presenting a comprehensive study of the Poisson-Dirichlet distribution, this volume emphasizes recent progress in evolutionary dynamics and asymptotic behaviors. The self-contained text presents methods and techniques that appeal to researchers in a wide variety of subjects.