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ISBN 10: 9810245912
ISBN 13: 9789810245917
Author: Hiroshi Tanaka, Makoto Maejima, Tokuzo Shiga, Makoto Maejima, Tokuzo Shiga
Hiroshi Tanaka is noted for his discovery of the “Tanaka formula”, which is a generalization of the Itô formula in stochastic analysis. This important book is a selection of his brilliant works on stochastic processes and related topics. It contains Tanaka's papers on (i) Brownian motion and stochastic differential equations (additive functionals of Brownian paths and stochastic differential equations with reflecting boundaries), (ii) the probabilistic treatment of nonlinear equations (Boltzmann equation, propagation of chaos and McKean-Vlasov limit), and (iii) stochastic processes in random environments (especially limit theorems on the stochastic processes in one-dimensional random environments and their refinements). The book also includes essays by Henry McKean, Marc Yor, Shinzo Watanabe and Hiroshi Tanaka on Tanaka's works.
1. INTRODUCTION.
2. BROWNIAN MOTION.
3. THE ASSOCIATED MEASURE OF AN ADDITIVE FUNCTIONAL.
4. UNIQUENESS.
5. CONSTRUCTION OF AN ADDITIVE FUNCTIONAL FROM ITS ASSOCIATED MEASURE.
6. DIFFUSIONS WITH BROWNIAN HITTING PROBABILITIES.
7. SPEED MEASURES
8 TWO DIFFUSIONS WITH BROWNIAN HITS AND THE SAME SPEED MEASURE ARE THE SAME.
9. SPEED MEASURES ARE POSITIVE ON FINE NEIGHBORHOODS.
10. SPEED MEASURES GIVE RISE TO INCREASING ADDITIVE FUNCTIONALS.
11. WHEN IS f(+oo)= +oo?
12. PERFORMING THE TIME SUBSTITUTION.
13. GENERATORS.
14. DISCONTINUOUS ADDITIVE FUNCTIONALS.
probability and stochastic processes
probability random variables and stochastic processes
introduction to stochastic processes
probability theory and stochastic processes
introduction to stochastic processes with r
applied stochastic processes
Tags: Hiroshi Tanaka, Makoto Maejima, Tokuzo Shiga, Makoto Maejima, Tokuzo Shiga, Stochastic, processes
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