Strengthening the weak convergence of random processes

1976 ◽  
Vol 17 (1) ◽  
pp. 16-22
Author(s):  
V. M. Borodikhin
Keyword(s):  
Weak Convergence ◽  
Random Processes

scholarly journals Weak convergence of random processes with immigration at random times

2020 ◽  
Vol 57 (1) ◽  
pp. 250-265
Author(s):  
Congzao Dong ◽  
Alexander Iksanov
Keyword(s):  
Weak Convergence ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Random Processes ◽  
Branching Random Walk ◽  
General Point ◽  
Shot Noise Process ◽  
Finite Dimensional ◽  
Strong Resemblance ◽  
Random Times

AbstractBy a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. Such random processes generalize random processes with immigration at the epochs of a renewal process which were introduced in Iksanov et al. (2017) and bear a strong resemblance to a random characteristic in general branching processes and the counting process in a fixed generation of a branching random walk generated by a general point process. We provide sufficient conditions which ensure weak convergence of finite-dimensional distributions of these processes to certain Gaussian processes. Our main result is specialised to several particular instances of random times and response processes.

scholarly journals On the weak convergence of vector-valued continuous random processes

1998 ◽  
Vol 43 (3) ◽  
pp. 561-576
Author(s):  
Su Zhong Gen ◽  
Su Zhong Gen ◽  
Su Zhong Gen ◽  
Su Zhong Gen
Keyword(s):  
Weak Convergence ◽  
Random Processes ◽  
Vector Valued
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