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An introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case in order to quickly progress to the parts of the theory that are most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are
An introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to
Provides a quick, but very readable introduction to stochastic differential equations-that is, to differential equations subject to additive 'white noise' and related random disturbances. The exposition is strongly focused upon the interplay between probabilistic intuition and mathematical
Provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership. The book presents an outline of the underlying convergence and stability theory while avoiding technical
Markov processes.- Stochastic Differential Equations and Martingale Problems.- Stochastic Filtering.- Static Markov Bridges and Enlargement of Filtrations.- Dynamic Bridges.- Financial markets with informational asymmetries and equilibrium.- Kyle-Back model with dynamic information: no default
This text provides an introduction to partial differential equations and boundary value problems, including Fourier series. The treatment offers students a smooth transition from a course in elementary ordinary differential equations to more advanced topics in a first course in partial differential
Hirsch, Devaney, and Smale's classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and
Modelling with the Itô integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory.This book is suitable for the reader without a
Preface.- 1.Differential Equations with Given Partial and First Integrals.- 2.Polynomial Vector Fields with Given Partial and First Integrals.- 3.16th Hilbert Problem for Algebraic Limit Cycles.- 4.Inverse Problem for Constrained Lagrangian Systems.- 5.Inverse Problem for Constrained Hamiltonian
This book is an introduction to stochastic analysis and quantitative finance; Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical
Version 6.5. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra
Hailed by The American Mathematical Monthly as a rigorous and lively introduction, this text explores a topic of perennial interest in mathematics. The author, a distinguished mathematician and formulator of the Hurewicz theorem, presents a clear and lucid treatment that emphasizes geometric
Make sense of these difficult equations Improve your problem-solving skills Practice with clear, concise examples Score higher on standardized tests and exams Get the confidence and the skills you need to master differential equations Need to know how to solve differential equations? This
Symmetry methods have long been recognized to be of great importance for the study of the differential equations. This book provides a solid introduction to those applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented
An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years
Nuclear Energy: An Introduction to the Concepts, Systems, and Applications of Nuclear Processes, Eighth Edition, provides essential information on basic nuclear physics, systems and the applications of nuclear energy. It comprehensively covers Basic Concepts, Radiation and Its Uses, and Nuclear
A vigorous response to the challenges of incorporating computer use into the teaching and learning of stochastic processes, this book takes an applications- and computer-oriented approach rather than the standard formal and mathematically rigorous approach. It is suitable for advanced
An informal and easy-to-understand introduction to digital signal processing, this treatment emphasizes digital audio and applications to computer music. Topics include: - Phasors and tuning forks - The wave equation - Sampling and quantizing - Feedforward and feedback filters - Comb and
This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence and stresses the global aspects of cosmology. 1979
This text covers topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, tangent spaces, vector fields and integral curves, Whitney's embedding theorem, more. Includes 88 helpful illustrations. 1982