........ published in NEWSLETTER # 53
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........ published in NEWSLETTER # 53
STOCHASTIC ANALYSIS AND APPLICATIONS IN PHYSICS
by Dr. L. Streit, Centre of Mathematical Sciences, Funchal/Madeira (Portugal)
Stochastic analysis and its various applications in physics have to a large extent developed symbiotically. In the past, mathematics has provided physics with a vast and rapidly expanding array of structures and methods, while on the other hand physics has counted prominently among the sources of direction and structural intuition the mathematical researchi n stochastics.
The present volume (NATO ASI SERIES C449) tries to capture some of the focal points of this dialogue. On the mathematical side, White Noise Analysis is being presented _ and applied by T. Hida and L. Streit. Another mathematical growth point is the theory of stochastic differential equations, presented (again including applications) by Jona_Lasinio et al., and by Oksendal, Potthof, Russo and Seneor. Gauge field theories have attracted the attention of both mathematicians and physicists (Gross, Leandre, Sengupta). Contributions on stochastic techniques in computational quantum field theory by Lang and in condensed matter physics by Vilela Mendes illustrate the role of stochastic methods in modern theoretical physics. Dirichlet forms an important link between the dynamics of quantum systems, and the mathematical theory of Markov processes are coverd by Albeverio et al. Collet and Mandreker address the conceptually important deterministic_ stochastic interface, while Cruzeiro and Zambrini introduce Bernstein processes for Euclidean quantum mechanics. Finally there are contributions by Truman on excursions of diffusion processes and by Streater on Kubo_ Martin_Schwinger norms in statistical mechanics.
In conclusion, the lectures in this volume offer a gateway to a field of modern research experiencing lively development, and under the guidance of acknowledged leaders in the field.
Reference books: B258, C78, C84, C104, C200, C372, C449