Local limit theorems for functionals in the conditional invariance principle

Journal of Mathematical Sciences - Tập 43 - Trang 2764-2768 - 1988
P. Breier

Tóm tắt

We prove the strong convergence of distributions of a large class of functionals of random polygonal paths constructed from independent, identically distributed variables.

Tài liệu tham khảo

I. S. Borisov, “Rate of convergence in the conditional invariance principle,” Teor. Veroyatn. Primen.,23, No. 1, 67–79 (1978). Yu. A. Davydov, “Strong convergence of distributions of functionals of stochastic processes, I, II,” Teor. Veroyatn. Primen.,25, No. 4, 782–799 (1980);26, No. 2, 266–286 (1981). Yu. A. Davydov, “Local invariance principle, I, II,” J. Sov. Math.,24, No. 5 (1984);22, No. 6 (1984). Yu. A. Davydov, “Local limit theorems for functionals of Gaussian processes,” Teor. Veroyatn. Primen.,26, No. 4, 870–871 (1981). Yu. A. Davydov, “Local limit theorems for functionals of stochastic processes,” Teor. Veroyatn. Primen.,22, No. 2 (1987). Yu. A. Davydov and M. A. Lifshits, “Stratification methods in some probabilistic problems,” Itogi Nauki Tekh., VINITI, Seriya Teor. Veroyatn. Mat. Statist., Teor. Kibern.,22, 61–157 (1984). I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Related Variables [in Russian], Moscow (1965).