This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology.
This volume develops results on continuous time branching processes and applies them to study rate of tumor growth, extending classic work on the Luria-Delbruck distribution.
This volume features a collection of contributed articles and lecture notes from the XI Symposium on Probability and Stochastic Processes, held at CIMAT Mexico in September 2013.
Providing a self-contained resource for upper undergraduate courses in combinatorics, this text emphasizes computation, problem solving, and proof technique.
This book constitutes the refereed proceedings of the 13th International Scientific Conference on Information Technologies and Mathematical Modeling, named after A.
Focusing on two central conjectures of Asymptotic Geometric Analysis, the Kannan-Lovasz-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the treated topics.
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena.
In this second volume, a general approach is developed to provide approximate parameterizations of the "e;small"e; scales by the "e;large"e; ones for a broad class of stochastic partial differential equations (SPDEs).
This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations.
This Festschrift in honour of Paul Deheuvels' 65th birthday compiles recent research results in the area between mathematical statistics and probability theory with a special emphasis on limit theorems.
The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction.
This is the revised and enlarged 2nd edition of the authors' original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory.
Many results, both from semi group theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community.
Providing a broad overview of the current state of the art in probability theory and its applications, and featuring an article coauthored by Mark Yor, this volume contains contributions on branching processes, Levy processes, random walks and martingales and their connection with, among other topics, rough paths, semi-groups, heat kernel asymptotics and mathematical finance.
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.
