Limit theorems are proved establishing criteria of convergence of the distributions of random sums and statistics constructed from samples with random sizes to exponential power laws. INTRODUCTION. EXPONENTIAL POWER DISTRIBUTIONS Let 0 < α 6 2. Exponential power distribution is the absolutely continuous distribution defined by its Lebesgue probability density

We show that a large class of stationary continuous-time regenerative processes are finitarily isomorphic to one another. The key is showing any renewal point process whose jump distribution absolutely continuous with exponential tails Poisson process. further give simple necessary and sufficient conditions for be This improves results answers several questions Soo [33] Kosloff [19].