This volume will be useful to graduate students and research mathematicians wishing to get acquainted with recent developments in the field of stochastic analysis.
During the last thirty years the use of nonstandard models in mathematics has taken its rightful place among the various methods employed by mathematicians. The contributions in this volume have been selected to present a panoramic view of the various directions in which nonstandard analysis is advancing, thus serving as a source of inspiration for future research.
Papers have been grouped in sections dealing with analysis, topology and topological groups; probability theory; and mathematical physics.
This volume can be used as a complementary text to courses in nonstandard analysis, and will be of interest to graduate students and researchers in both pure and applied mathematics and physics.
• Time and physics
• Time, philosophy and psychology
• Time, mathematics and information theory
It is a unique contribution by philosophers and scientists who are active in mathematics, physics, biology, engineering, information theory and psychology. Questions such as the existence of a Big Bang, the neurobiological basis regarding the coexistence of free will and determinism, intercultural aspects of time, mathematical models of time, psychopathological features of time, and micro reversibility versus macroscopic irreversibility are studied. It also provides a truly interdisciplinary study of the problematic 'arrow of time'.
The present monograph provides a thorough treatment of the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes, and summarizes in an epilogue the model-theoretic genericity of hyperfinite stochastic processes theory.