摘要: Many useful descriptions of stochastic models can be obtained from functional limit theorems invariance principles or weak convergence for probability measures on function spaces. These typically come standard via the continuous mapping theorem. This paper facilitates applications theorem by determining when several important functions and sequences preserve convergence. The considered are composition, addition, composition plus multiplication, supremum, reflecting barrier, first passage time reversal. provide means proving new previous ones. useful, example, to establish stability continuity queues other models.
core.ac.uk
columbia.edu 
jstor.org 
sci-hub.se 参考文章(30)
Torgny Lindvall, Weak convergence of probability measures and random functions in the function space D[0,∞) Journal of Applied Probability. ,vol. 10, pp. 109- 121 ,(1973) , 10.2307/3212499
Miron L. Straf, Weak convergence of stochastic processes with several parameters Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume 2: Probability Theory. ,(1972)
Laurent Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures ,(1973)
Patrick Billingsley, Weak Convergence of Measures: Applications in Probability ,(1987)
R. M. Dudley, Distances of Probability Measures and Random Variables Annals of Mathematical Statistics. ,vol. 39, pp. 28- 37 ,(1968) , 10.1007/978-1-4419-5821-1_4
N.R. Mohan, A note on the J1-convergence of a first-passage process Stochastic Processes and their Applications. ,vol. 4, pp. 157- 165 ,(1976) , 10.1016/0304-4149(76)90033-8
D. J. Aldous, Weak convergence of randomly indexed sequences of random variables Mathematical Proceedings of the Cambridge Philosophical Society. ,vol. 83, pp. 117- 126 ,(1978) , 10.1017/S0305004100054359
Donald L. Iglehart, Ward Whitt, Multiple channel queues in heavy traffic. II: sequences, networks, and batches Advances in Applied Probability. ,vol. 2, pp. 355- 369 ,(1970) , 10.2307/1426324
Richard T. Durrett, Sidney I. Resnick, Weak convergence with random indices Stochastic Processes and their Applications. ,vol. 5, pp. 213- 220 ,(1977) , 10.1016/0304-4149(77)90031-X
Michael J. Wichura, ON THE CONSTRUCTION OF ALMOST UNIFORMLY CONVERGENT RANDOM VARIABLES WITH GIVEN WEAKLY CONVERGENT IMAGE LAWS Annals of Mathematical Statistics. ,vol. 41, pp. 284- 291 ,(1970) , 10.1214/AOMS/1177697207