Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation.
Articles from many of the main contributors to recent progress in stochastic analysis are included in this volume, which provides a snapshot of the current state of the area and its ongoing developments.
This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals.
The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains.
This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.
This title takes an in-depth look at the mathematics in the context of voting and electoral systems, with focus on simple ballots, complex elections, fairness, approval voting, ties, fair and unfair voting, and manipulation techniques.
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes).
This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed.
This monograph introduces methods for handling filtering and control problems in nonlinear stochastic systems arising from network-induced phenomena consequent on limited communication capacity.
The aim of this book is to summarize probabilistic safety assessment (PSA) of nuclear power plants with WWER440 reactors and demonstrate that the plants are safe enough for producing energy even in light of the Fukushima accident.
Lyons' rough path analysis has provided new insights in the analysis of stochastic differential equations and stochastic partial differential equations, such as the KPZ equation.
In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 "e;Mathematical Methods for Extracting Quantifiable Information from Complex Systems.
This book presents a forecasting mechanism of the price intervals for deriving the SCR (solvency capital requirement) eradicating the risk during the exercise period on one hand and measuring the risk by computing the hedging exit time function associating with smaller investments the date until which the value of the portfolio hedges the liabilities on the other.
The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates.
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions.
The dynamics of population systems cannot be understood within the framework of ordinary differential equations, which assume that the number of interacting agents is infinite.
Probability theory on compact Lie groups deals with the interaction between "e;chance"e; and "e;symmetry,"e; a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing).
This volumepresents a collection of papers covering applications from a wide range ofsystems with infinitely many degrees of freedom studied using techniques fromstochastic and infinite dimensional analysis, e.
This book brings theories in nonlinear dynamics, stochastic processes, irreversible thermodynamics, physical chemistry and biochemistry together in an introductory but formal and comprehensive manner.
Containing a summary of several recent results on Markov-based input modeling in a coherent notation, this book introduces and compares algorithms for parameter fitting and gives an overview of available software tools in the area.
This book is a compilation of 21 papers presented at the International Cramer Symposium on Insurance Mathematics (ICSIM) held at Stockholm University in June, 2013.
The classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory.
This monograph serves as an introductory text to classical renewal theory and some of its applications for graduate students and researchers in mathematics and probability theory.
The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book.
This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics.
This volume of the Selected Papers is a product of the XIX Congress of the Portuguese Statistical Society, held at the Portuguese town of Nazare, from September 28 to October 1, 2011.
This text is for a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful tests and the Neyman Pearson Lemma.
The problem of probability interpretation was long overlooked before exploding in the 20th century, when the frequentist and subjectivist schools formalized two conflicting conceptions of probability.
The work consists of two introductory courses, developing different points of view on the study of the asymptotic behaviour of the geodesic flow, namely: the probabilistic approach via martingales and mixing (by Stephane Le Borgne); the semi-classical approach, by operator theory and resonances (by Frederic Faure and Masato Tsujii).
This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions.
Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics.
This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes.
These lecture notes provide an introduction to the applications of Brownian motion to analysis and more generally, connections between Brownian motion and analysis.
A certain curious feature of random objects, introduced by the author as "e;super concentration,"e; and two related topics, "e;chaos"e; and "e;multiple valleys,"e; are highlighted in this book.
In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits.
This volume presents recent developments in the area of Levy-type processes and more general stochastic processes that behave locally like a Levy process.
The goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of strongly dependent random variables that play an important role in probability theory or in statistical physics.
In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting.
