The book deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up.
This richly illustrated book is an exploration of how chance and risk, on the one hand, and meaning or significance on the other, compete for the limelight in art, in philosophy, and in science.
It was the end of 2005 when our employer, a major European Investment Bank, gave our team the mandate to compute in an accurate way the counterparty credit exposure arising from exotic derivatives traded by the ?
Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics.
Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology.
In modern financial practice, asset prices are modelled by means of stochastic processes, and continuous-time stochastic calculus thus plays a central role in financial modelling.
Objectives and Audience In the past three decades, we have witnessed the phenomenal growth in the trading of financial derivatives and structured products in the financial markets around the globe and the surge in research on derivative pricing theory.
This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists.
This volume represents a part of the main result obtained bya group of French probabilists, together with thecontributions of a number of colleagues, mainly from the USAand Japan.
In three chapters on Exponential Martingales, BMO-martingales, and Exponential of BMO, this book explains in detail the beautiful properties of continuous exponential martingales that play an essential role in various questions concerning the absolute continuity of probability laws of stochastic processes.
The 2-volume book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research.
The theory of Dirichlet forms has witnessed recently somevery important developments both in theoretical foundationsand in applications (stochasticprocesses, quantum fieldtheory, composite materials,.
In this volume of original research papers, the main topics discussed relate to the asymptotic windings of planar Brownian motion, structure equations, closure properties of stochastic integrals.
This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field.
The subject of this book is a new direction in the field ofprobability theory and mathematical statistics which can becalled "e;stability theory"e;: it deals with evaluating theeffects of perturbing initial probabilistic models andembraces quite varied subtopics: limit theorems, queueingmodels, statistical inference, probability metrics, etc.
The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc.
The problem of designing a cost-efficient network thatsurvives the failure of one or more nodes or edges of thenetwork is critical to modern telecommunicationsengineering.
Traditionally the Stability seminar, organized in Moscow but held in different locations, has dealt with a spectrum of topics centering around characterization problems and their stability, limit theorems, probabil- ity metrics and theoretical robustness.
This book contains three lectures each of 10 sessions; the first on Potential Theory on graphs and manifolds, the second on annealing and another algorithms for image reconstruction, the third on Malliavin Calculus.
This volume, the fourth of the quantum probability series, collects part of the contributions to the Year of Quantum Probability organized by the Volterra Center of University of Rome II.
Entropy inequalities, correlation functions, couplingsbetween stochastic processes are powerful techniques whichhave been extensively used to give arigorous foundation tothe theory of complex, many component systems and to itsmany applications in a variety of fields as physics,biology, population dynamics, economics, .
Focussing on the interrelations of the subjects of Markov processes, analytic semigroups and elliptic boundary value problems, this monograph provides a careful and accessible exposition of functional methods in stochastic analysis.
The interplay between the spectral theory of Schr|dingeroperators and probabilistic considerations forms the maintheme of these notes, written for the non-specialist readerand intended to provide a brief and elementaryintroductionto this field.
The Second Silivri Workshop functioned as a short summer school and a working conference, producing lecture notes and research papers on recent developments of Stochastic Analysis on Wiener space.
The purpose of the conference was to represent recentdevelopments in measure theoretic, differentiable andtopological dynamical systems as well as connections toprobability theory, stochastic processes, operator theoryand statistical physics.
