Two Problems In The Theory Of Probability And Stochastic Process

The first part of this paper is to give a new proof of the construction of the Cauchy Process on the circle. The second part is the topic on the inverse problems of the maximum entropy principle. With the assumption of the maximum entropy, we can obtain the constraint conditions under which the entropy is maximum for some probability density functions, As concrete problems, we deal with the binomial distribution, normal distribution and logarithmic normal distribution, Gamma-distribution, Weibull distribution and levy distribution and so on.