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Dirichlet Forms and Stochastic Processes
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Stochastic Processes, Physics and Geometry: New Interplays. I
A selection of 21 contributions from invited speakers treat advanced topics at the interface between mathematics and physics. Most are high-level research papers, but some overview their topics, among which are growth and saturation in random media, the maximal dissipativity of the Dirichlet operator corresponding to the Burgers equation, the square of the self-intersection local time of Brownian motion, the spectral theory of sparse potentials, and diffusions on simple configuration spaces. Additional short contributions pay tribute to Swiss-born physicist Albeverio. A second volume presents selected volunteer papers. There is no index. Annotation copyrighted by Book News, Inc., Portland, OR
Stochastic Processes, Physics and Geometry: New Interplays. II
The second of two volumes with selected treatments of the conference theme, Infinite Dimensional (Stochastic) Analysis and Quantum Physics, which positions scientists at the interface of mathematics and physics. The 57 papers discuss such topics as the valuation of bonds and options under floating interest rate, the loop group factorization of biorthogonal wavelet bases, asymptotic properties of the maximal sub-interval of a Poisson process, generalized configuration spaces for quantum systems, Sobolev spaces and the capacity theory of path spaces, representing coherent state in white noise calculus, and the analytic quantum information manifold. There is no index. The first volume contains contributions of invited speakers. Annotation copyrighted by Book News, Inc., Portland, OR
Lévy Processes and Stochastic Calculus
Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
Pseudo Differential Operators and Markov Processes
After recalling essentials of analysis OCo including functional analysis, convexity, distribution theory and interpolation theory OCo this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students. Sample Chapter(s). Introduction: Pseudo Differential Operators and Markov Processes (207 KB). Chapter 1: Introduction (190 KB). Contents: Essentials from Analysis: Calculus Results...
Lévy Matters VI
Presenting some recent results on the construction and the moments of Lévy-type processes, the focus of this volume is on a new existence theorem, which is proved using a parametrix construction. Applications range from heat kernel estimates for a class of Lévy-type processes to existence and uniqueness theorems for Lévy-driven stochastic differential equations with Hölder continuous coefficients. Moreover, necessary and sufficient conditions for the existence of moments of Lévy-type processes are studied and some estimates on moments are derived. Lévy-type processes behave locally like Lévy processes but, in contrast to Lévy processes, they are not homogeneous in space. Typical examples are processes with varying index of stability and solutions of Lévy-driven stochastic differential equations. This is the sixth volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject, with special emphasis on the non-Brownian world.
Pseudo Differential Operators And Markov Processes, Volume I: Fourier Analysis And Semigroups
After recalling essentials of analysis — including functional analysis, convexity, distribution theory and interpolation theory — this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students./a
