Stochastic Processes: Selected Papers On Hiroshi Tanaka

Hiroshi Tanaka is noted for his discovery of the Tanaka Formula , which is a generalization of the Ito formula in stochastic analysis. This 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 volume also includes essays by Henry McKean, Marc Yor, Shinzo Watanabe and Hiroshi Tanaka on Tanaka’s works.