Author: Henryk Gzyl
Publisher: Springer
Keywords: applications, mathematics, waves, diffusions
Number of Pages: 244
Published: 2002-11-30
List price: unknow
ISBN-10: 1402009674
ISBN-13: 9781402009679

In this book several connections between probability theory and wave propagation are explored. The connection comes via the probabilistic (or path integral) representation of both the (fixed frequency) Green functions and of the propagators -operators mapping initial into present time data. The formalism includes both waves in continuous space and in discrete structures. One of the main applications of the formalism developed is to inverse problems in wave propagation. Using the probabilistic formalism, the parameters of the medium and the surfaces determining the region of propagation appear

Author: Richard F. Ba
Publisher: Springer
Keywords: applications, probability, operators, elliptic, diffusions
Number of Pages: 248
Published: 1997-11-25
List price: $159.00
ISBN-10: 0387983155
ISBN-13: 9780387983158

This book discusses the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods in PDE. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE. After spending three chapters on probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions, the author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-d

Authors:Wei-Ming Ni, L.A. Peletier, J.L. Vazquez,
Publisher: Springer
Keywords: mathematics, applications, volumes, ima, diffusions, degenerate
Number of Pages: 252
Published: 1993-06-24
List price: $109.00
ISBN-10: 0387940685
ISBN-13: 9780387940687

This volume is the proceedings of the IMA workshop "Degenerate Diffusions" held at the University of Minnesota from May 13-May 18, 1991. The workshop consisted of two parts. The emphasis of the first four days was on current progress or new problems in nonlinear diffusions involving free boundaries or sharp interfaces. Analysts and geometers will find some of the mathematical models described in this volume interesting; and the papers of more pure mathematical nature included here should provide applied mathematicians with powerful methods and useful techniques in handling singular perturbatio

Author: Panagiota Daskalopoulos and Carlos E. Kenig
Publisher: European Mathematical Society
Keywords: mathematics, tracts, ems, diffusions, degenerate
Number of Pages: 207
Published: 2007-05-15
List price: $62.00
ISBN-10: 3037190337
ISBN-13: 9783037190333

The book deals with the existence, uniqueness, regularity, and asymptotic behavior of solutions to the initial value problem (Cauchy problem) and the initial-Dirichlet problem for a class of degenerate diffusions modeled on the porous medium type equation $u_t = Delta u^m$, $m geq 0$, $u geq 0$. Such models arise in plasma physics, diffusion through porous media, thin liquid film dynamics, as well as in geometric flows such as the Ricci flow on surfaces and the Yamabe flow. The approach presented to these problems uses local regularity estimates and Harnack type inequalities, which yield compa

Authors:Bernt Øksendal, Agnès Sulem,
Publisher: Springer
Keywords: diffusions, universitext, jump, control, stochastic, applied
Number of Pages: 262
Published: 2007-06-28
List price: $59.95
ISBN-10: 3540698256
ISBN-13: 9783540698258

The main purpose of the book is to give a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Both the dynamic programming method and the maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities are formulated. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end o

Authors:L. C. G. Rogers, David Williams,
Publisher: Cambridge University Press
Keywords: calculus, cambridge, mathematical, library, itã´, volume, markov, processes, martingales, diffusions
Number of Pages: 494
Published: 2000-09-18
List price: $67.00
ISBN-10: 0521775930
ISBN-13: 9780521775939

The second volume concentrates on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. These subjects are made accessible in the many concrete examples that illustrate techniques of calculation, and in the treatment of all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appear for the first time in this book.

Authors:L. C. G. Rogers, David Williams,
Publisher: Cambridge University Press
Keywords: cambridge, mathematical, library, foundations, volume, markov, processes, martingales, diffusions
Number of Pages: 406
Published: 2000-05-01
List price: $67.00
ISBN-10: 0521775949
ISBN-13: 9780521775946

Now available in paperback, this celebrated book remains a key systematic guide to a large part of the modern theory of Probability. The authors not only present the subject of Brownian motion as a dry part of mathematical analysis, but convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively presentation of the theory of Markov processes. Together with its companion volume, this book equips graduate students for research in