Download or read book A Minicourse on Stochastic Partial Differential Equations written by Robert C. Dalang and published by Springer Science & Business Media. This book was released on 2009 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title contains lectures that offer an introduction to modern topics in stochastic partial differential equations and bring together experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic PDEs.

Download or read book Interest Rate Models an Infinite Dimensional Stochastic Analysis Perspective written by René Carmona and published by Springer Science & Business Media. This book was released on 2007-05-22 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical issues that arise in modeling the interest rate term structure by casting the interest-rate models as stochastic evolution equations in infinite dimensions. The text includes a crash course on interest rates, a self-contained introduction to infinite dimensional stochastic analysis, and recent results in interest rate theory. From the reviews: "A wonderful book. The authors present some cutting-edge math." --WWW.RISKBOOK.COM

Download or read book Stochastic Climate Models written by Peter Imkeller and published by Birkhäuser. This book was released on 2012-12-06 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles written by mathematicians and physicists, designed to describe the state of the art in climate models with stochastic input. Mathematicians will benefit from a survey of simple models, while physicists will encounter mathematically relevant techniques at work.

Download or read book Stochastic Partial Differential Equations An Introduction written by Wei Liu and published by Springer. This book was released on 2015-10-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and the ‘locally monotone case’ is presented in a detailed and complete way for SPDEs. The extension to this more general framework for SPDEs, for example, in comparison to the well-known case of globally monotone coefficients, substantially widens the applicability of the results.

Download or read book Multiparameter Processes written by Davar Khoshnevisan and published by Springer Science & Business Media. This book was released on 2006-04-10 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-contained presentation: from elementary material to state-of-the-art research; Much of the theory in book-form for the first time; Connections are made between probability and other areas of mathematics, engineering and mathematical physics

Download or read book A Course on Rough Paths written by Peter K. Friz and published by Springer Nature. This book was released on 2020-05-27 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH

Download or read book An Introduction to Stochastic Differential Equations with Reflection written by Andrey Pilipenko and published by Universitätsverlag Potsdam. This book was released on 2014 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Analysis and Applications to Finance written by Tusheng Zhang and published by World Scientific. This book was released on 2012 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. The articles represent new directions and newest developments in this exciting and fast growing area. The covered topics range from Markov processes, backward stochastic differential equations, stochastic partial differential equations, stochastic control, potential theory, functional inequalities, optimal stopping, portfolio selection, to risk measure and risk theory. It will be a very useful book for young researchers who want to learn about the research directions in the area, as well as experienced researchers who want to know about the latest developments in the area of stochastic analysis and mathematical finance. Sample Chapter(s). Editorial Foreword (58 KB). Chapter 1: Non-Linear Evolution Equations Driven by Rough Paths (399 KB). Contents: Non-Linear Evolution Equations Driven by Rough Paths (Thomas Cass, Zhongmin Qian and Jan Tudor); Optimal Stopping Times with Different Information Levels and with Time Uncertainty (Arijit Chakrabarty and Xin Guo); Finite Horizon Optimal Investment and Consumption with CARA Utility and Proportional Transaction Costs (Yingshan Chen, Min Dai and Kun Zhao); MUniform Integrability of Exponential Martingales and Spectral Bounds of Non-Local Feynman-Kac Semigroups (Zhen-Qing Chen); Continuous-Time Mean-Variance Portfolio Selection with Finite Transactions (Xiangyu Cui, Jianjun Gao and Duan Li); Quantifying Model Uncertainties in the Space of Probability Measures (J Duan, T Gao and G He); A PDE Approach to Multivariate Risk Theory (Robert J Elliott, Tak Kuen Siu and Hailiang Yang); Stochastic Analysis on Loop Groups (Shizan Fang); Existence and Stability of Measure Solutions for BSDE with Generators of Quadratic Growth (Alexander Fromm, Peter Imkeller and Jianing Zhang); Convex Capital Requirements for Large Portfolios (Hans FAllmer and Thomas Knispel); The Mixed Equilibrium of Insider Trading in the Market with Rational Expected Price (Fuzhou Gong and Hong Liu); Some Results on Backward Stochastic Differential Equations Driven by Fractional Brownian Motions (Yaozhong Hu, Daniel Ocone and Jian Song); Potential Theory of Subordinate Brownian Motions Revisited (Panki Kim, Renming Song and Zoran Vondraiek); Research on Social Causes of the Financial Crisis (Steven Kou); Wick Formulas and Inequalities for the Quaternion Gaussian and -Permanental Variables (Wenbo V Li and Ang Wei); Further Study on Web Markov Skeleton Processes (Yuting Liu, Zhi-Ming Ma and Chuan Zhou); MLE of Parameters in the Drifted Brownian Motion and Its Error (Lemee Nakamura and Weian Zheng); Optimal Partial Information Control of SPDEs with Delay and Time-Advanced Backward SPDEs (Bernt yksendal, Agn s Sulem and Tusheng Zhang); Simulation of Diversified Portfolios in Continuous Financial Markets (Eckhard Platen and Renata Rendek); Coupling and Applications (Feng-Yu Wang); SDEs and a Generalised Burgers Equation (Jiang-Lun Wu and Wei Yang); Mean-Variance Hedging in the Discontinuous Case (Jianming Xia). Readership: Graduates and researchers in stochatic analysis and mathematical finance.

Download or read book Stochastic Partial Differential Equations written by Sergey V. Lototsky and published by Springer. This book was released on 2017-07-06 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed. The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.

Download or read book Introduction to Malliavin Calculus written by David Nualart and published by Cambridge University Press. This book was released on 2018-09-27 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.

Download or read book Stochastic Partial Differential Equations and Related Fields written by Andreas Eberle and published by Springer. This book was released on 2018-07-03 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.

Download or read book Analysis of Stochastic Partial Differential Equations written by Davar Khoshnevisan and published by American Mathematical Soc.. This book was released on 2014-06-11 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a "random noise," also known as a "generalized random field." At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals à la Norbert Wiener, an infinite-dimensional Itô-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts. There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation. A co-publication of the AMS and CBMS.

Download or read book Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA written by Elias T. Krainski and published by CRC Press. This book was released on 2018-12-07 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

Download or read book Effective Dynamics of Stochastic Partial Differential Equations written by Jinqiao Duan and published by Elsevier. This book was released on 2014-03-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. - New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty - Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations - Solutions or hints to all Exercises

Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer. This book was released on 2010-08-18 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Download or read book An Introduction to Computational Stochastic PDEs written by Gabriel J. Lord and published by Cambridge University Press. This book was released on 2014-08-11 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB® codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science.

Download or read book Mathematical Control Theory for Stochastic Partial Differential Equations written by Qi Lü and published by Springer Nature. This book was released on 2021-10-19 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.