Series: De Gruyter Textbook
Organizes the subject on three levels: classical, modern and semi-linear theory
Clearly explains the transition from classical to generalized solutions
Introduces, in the beginning, the Sobolev spaces as completions of spaces of continuously differentiable functions with respect to energetic norms
Presents the solution operators associated to non-homogeneous equations and anticipates the operator method for nonlinear problems
Covers most of the main topics usually studied in standard courses
Provides a rigorous theoretical treatment by organizing the material around theorems and proofs
Includes numerous exercises and problems to assimilate and extend the theory
Provides a solid base for further study and inspiration for future research in the field
Provides material for three one-semester courses: a beginner, an advanced and a master course
The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs. Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of nonlinear analysis. Compared to other introductory books in PDEs, this work clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions with respect to energetic norms. Also, special attention is paid to the investigation of the solution operators associated to elliptic, parabolic and hyperbolic non-homogeneous equations anticipating the operator approach of nonlinear boundary value problems. Thus the reader is made to understand the role of linear theory for the analysis of nonlinear problems.
Series: De Gruyter Textbook
OverviewDetailsAdditional InformationComments (2)Gently introduces stochastic processes addressing a wide audience comprising mathematicians, economists, engineers and scientists
Appropriate as a textbook for graduate courses, reading courses or for independent study
Includes modular chapters and a "dependence chart" which will guide the readers when arranging their own digest of material
More than 200 exercises (with solutions on the internet) help beginners to understand the material
Brownian motion is one of the most imposrtant stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance.
Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authorsf aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs.
This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.
Series: De Gruyter Proceedings in Mathematics
This is a proceeding of the international conference "Painleve Equations and Related Topics" which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the Steklov Institute of Mathematics of the Russian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011.
The survey articles discuss the following topics:
General ordinary differential equations
Painleve equations and their generalizations
Painleve property
Discrete Painleve equations
Properties of solutions of all mentioned above equations:
* Asymptotic forms and asymptotic expansions
* Connections of asymptotic forms of a solution near different points
* Convergency and asymptotic character of a formal solution
* New types of asymptotic forms and asymptotic expansions
* Riemann-Hilbert problems
* Isomonodromic deformations of linear systems
* Symmetries and transformations of solutions
? Algebraic solutions
Reductions of PDE to Painleve equations and their generalizations
Ordinary Differential Equations systems equivalent to Painleve equations and their generalizations
Applications of the equations and the solutions
Series: De Gruyter Proceedings in Mathematics
This is the proceedings of the VIII. IMACS Seminar on Monte Carlo Methods
2011, August 29 ? September 2, 2011, held in Borovets, Bulgaria, and organized by the Institute of Information and Communication Technologies,
Bulgarian Academy of Sciences in cooperation with International Association for Mathematics and Computers in Simulation (IMACS). Included are about 25 papers which cover all topics presented in the sessions of the Seminar: Stochastic Computation and Complexity of High Dimensional Problems, Sensitivity Analysis, High-performance Computations for Monte Carlo Applications, Stochastic Metaheuristics for Optimization Problems, Sequential Monte Carlo Methods for Large-scale Problems, Semiconductor Devices and Nanostructures.
The history of the IMACS Seminar on Monte Carlo Methods goes back to April 1997 when the first MCM Seminar was organized in Brussel
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Series: Inverse and Ill-Posed Problems Series 57
Solving inverse problems means the determination of shape or consistency of inaccessible objects from indirect measurements. Those problems arise in many applications, e.g., medical imaging and earth surface explorations. The mathematical modelling of some of those problems leads to inverse problems for boundary value problems for differential equations with incomplete given data. The present book provides an introduction to the numerical solution of the latter class of problems.