Analysis of stochastic processes on the adeles

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Construction of Markov processes on the adeles, and analysis of the distribution of the exit time from the p-adic integer ring, and the p-adic norm of the p-component of the processes at the exit time. Description of the distribution of the exit time of the adelic processes from the finite integral adeles. Formulae for Riemann's zeta and other functions with Euler product representations in terms of the exit time of the processes and the p-adic norm of the p-component at the exit time. Functional equations relating the values of Riemann's zeta function at a point and its complex conjugates or its real part.