Edited by: Ivan Ganchev Ivanov
ISBN 978-953-51-0830-6, Hard cover, 294 pages
Publication date: November 2012
Stochastic control plays an important role in many scientific and applied disciplines including communications, engineering, medicine, finance and many others. It is one of the effective methods being used to find optimal decision-making strategies in applications. The book provides a collection of outstanding investigations in various aspects of stochastic systems and their behavior. The book provides a self-contained treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, statistics, and computer science. Readers should be familiar with basic probability theory and have a working knowledge of stochastic calculus. PhD students and researchers in stochastic control will find this book useful.
Chapter 4, pp. 63-80,
Geometrical Derivation of Equilibrium Distributions in some Stochastic Systems,
Ricardo Lopez-Ruiz and Jaime Sañudo
Classical statistical physics deals with statistical systems in equilibrium. Two fundamental distributions to describe situations in equilibrium are the Boltzmann-Gibbs (exponential) distribution and the Maxwellian (Gaussian) distribution. The ﬁrst one represents the distribution of the energy states of a system and the second one ﬁts the distribution of velocities in an ideal gas. They can be explained from different perspectives. In this chapter, these distributions are obtained from a geometrical interpretation of different multi-agent systems evolving in phase space under the hypothesis of equiprobability. Alternatively, they can also be derived as the asymptotic equilibria of two nonlinear models recently proposed in the literature.