This book analyses selected algorithms for random and stochastic phenomena in the areas of basic probability, random variables, mathematical expectation, special probability and statistical distributions, random processes, and Markov chains. It also presents a novel approach, titled the “Complex Probability Paradigm”, and applies it to the Brownian motion. As such, the book will be of interest to all scholars, researchers, and undergraduate and graduate students in mathematics, computer science, and science in general.

In applied mathematics, the name Monte Carlo is given to the method of solving problems by means of experiments with random numbers. This name, after the casino at Monaco, was first applied around 1944 to the method of solving deterministic problems by reformulating them in terms of a problem with random elements, which could then be solved by large-scale sampling. But, by extension, the term has come to mean any simulation that uses random numbers. Monte Carlo methods have become among the most fundamental techniques of simulation in modern science. This book is an illustration of the use of Monte Carlo methods applied to solve specific problems in mathematics, engineering, physics, statistics, and science in general.

This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.

A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models in which a model represents the key characteristics or behaviors of the selected system or process and the simulation represents the evolution of the model over time. Computers are often used to execute simulations. This book provides a comprehensive overview of simulation modeling and explores its use to solve a large set of problems. It is a useful resource for scholars, researchers, and undergraduate and graduate students in pure and applied mathematics, physical sciences, engineering and technology, computer science, numerical analysis, scientific computing, and science in general.

This book constitutes the refereed proceedings of the 4th International Symposium on Stochastic Algorithms: Foundations and Applications, SAGA 2007. The nine revised full papers and five invited papers presented were carefully selected for inclusion in the book. The contributed papers included in this volume cover both theoretical as well as applied aspects of stochastic computations with a special focus on investigating the power of randomization in algorithmics.

Mathematical probability and statistics are an attractive, thriving, and respectable part of mathematics. Some mathematicians and philosophers of science say they are the gateway to mathematics’ deepest mysteries. Moreover, mathematical statistics denotes an accumulation of mathematical discussions connected with efforts to most efficiently collect and use numerical data subject to random or deterministic variations. Currently, the concept of probability and mathematical statistics has become one of the fundamental notions of modern science and the philosophy of nature. This book is an illustration of the use of mathematics to solve specific problems in engineering, statistics, and science in general.

This book constitutes the refereed proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications, SAGA 2001, held in Berlin, Germany in December 2001. The nine revised full papers presented together with four invited papers were carefully reviewed and selected for inclusion in the book. The papers are devoted to the design and analysis, experimental evaluation, and real-world application of stochasitc algorithms; in particular, new algorithmic ideas involving stochastic decisions and exploiting probabilistic properties of the underlying problem are introduced. Among the application fields are network and distributed algorithms, local search methods, and computational learning.

This book constitutes the refereed proceedings of the Second International Symposium on Stochastic Algorithms: Foundations and Applications, SAGA 2003, held in Hatfield, UK in September 2003. The 12 revised full papers presented together with three invited papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are ant colony optimization, randomized algorithms for the intersection problem, local search for constraint satisfaction problems, randomized local search and combinatorial optimization, simulated annealing, probabilistic global search, network communication complexity, open shop scheduling, aircraft routing, traffic control, randomized straight-line programs, and stochastic automata and probabilistic transformations.

Stochastic local search (SLS) algorithms are among the most prominent and successful techniques for solving computationally difficult problems. Offering a systematic treatment of SLS algorithms, this book examines the general concepts and specific instances of SLS algorithms and considers their development, analysis and application.