Weak convergence of probability measures and random functions in the function space D[0,∞)

1973 ◽  
Vol 10 (1) ◽  
pp. 109-121 ◽  
Author(s):  
Torgny Lindvall
Keyword(s):  
Weak Convergence ◽  
Function Space ◽  
Probability Measures ◽  
Applied Probability ◽  
Random Functions ◽  
Convergence Of Probability Measures ◽  
Suitable Space

This paper extends the theory of weak convergence of probability measures and random functions in the function space D[0,1] to the case D [0,∞), elaborating ideas of C. Stone and W. Whitt. 7)[0,∞) is a suitable space for the analysis of many processes appearing in applied probability.

Weak convergence of probability measures and random functions in the function space D[0,∞)

1973 ◽  
Vol 10 (01) ◽  
pp. 109-121 ◽  
Author(s):  
Torgny Lindvall
Keyword(s):  
Weak Convergence ◽  
Function Space ◽  
Probability Measures ◽  
Applied Probability ◽  
Random Functions ◽  
Convergence Of Probability Measures ◽  
Suitable Space

This paper extends the theory of weak convergence of probability measures and random functions in the function space D[0,1] to the case D [0,∞), elaborating ideas of C. Stone and W. Whitt. 7)[0,∞) is a suitable space for the analysis of many processes appearing in applied probability.

Weak convergence in queueing theory

1973 ◽  
Vol 5 (3) ◽  
pp. 570-594 ◽  
Author(s):  
Donald L. Iglehart
Keyword(s):  
Weak Convergence ◽  
Queueing Theory ◽  
Heavy Traffic ◽  
Rates Of Convergence ◽  
Probability Measures ◽  
Queueing Models ◽  
Applied Probability ◽  
Light Traffic ◽  
Survey Paper ◽  
Convergence Of Probability Measures

In the last ten years the theory of weak convergence of probability measures has been used extensively in studying the models of applied probability. By far the greatest consumer of weak convergence has been the area of queueing theory. This survey paper represents an attempt to summarize the experience in queueing theory with the hope that it will prove helpful in other areas of applied probability. The paper is organized into the following sections: queues in light traffic, queues in heavy traffic, queues with a large number of servers, continuity of queues, rates of convergence, and special queueing models.

Weak convergence in queueing theory

1973 ◽  
Vol 5 (03) ◽  
pp. 570-594 ◽  
Author(s):  
Donald L. Iglehart
Keyword(s):  
Weak Convergence ◽  
Queueing Theory ◽  
Heavy Traffic ◽  
Rates Of Convergence ◽  
Probability Measures ◽  
Queueing Models ◽  
Applied Probability ◽  
Light Traffic ◽  
Survey Paper ◽  
Convergence Of Probability Measures

In the last ten years the theory of weak convergence of probability measures has been used extensively in studying the models of applied probability. By far the greatest consumer of weak convergence has been the area of queueing theory. This survey paper represents an attempt to summarize the experience in queueing theory with the hope that it will prove helpful in other areas of applied probability. The paper is organized into the following sections: queues in light traffic, queues in heavy traffic, queues with a large number of servers, continuity of queues, rates of convergence, and special queueing models.

scholarly journals Value-distribution of twisted L-functions of normalized cusp forms

2010 ◽  
Vol 51 ◽  
Author(s):  
Alesia Kolupayeva
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Complex Plane ◽  
Dirichlet Character ◽  
Value Distribution ◽  
Cusp Forms ◽  
Probability Measures ◽  
Convergence Of Probability Measures

A limit theorem in the sense of weak convergence of probability measures on the complex plane for twisted with Dirichlet character L-functions of holomorphic normalized Hecke eigen cusp forms with an increasing modulus of the character is proved.

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