Weak convergence of random sums and maximum random sums under nonrandom norming

1996 ◽  
Vol 81 (5) ◽  
pp. 2957-2969
Author(s):  
V. M. Kruglov
Keyword(s):  
Weak Convergence ◽  
Random Sums

Weak Convergence of Distributions

2021 ◽  
pp. 495-519
Author(s):  
James Davidson
Keyword(s):  
Weak Convergence ◽  
Representation Theorem ◽  
Stable Distribution ◽  
Characteristic Functions ◽  
Random Sums ◽  
Skorokhod Representation Theorem

This chapter introduces the fundamentals of weak convergence for real sequences. Definitions and examples are given. The Skorokhod representation theorem is proved and the chapter then considers the preservation of weak convergence under transformations. Next, the role of moments and characteristic functions is considered. In the leading case of random sums, the criteria for weak convergence and the concept of a stable distribution are studied.

The Weak Convergence of Random Sums of ρ--Mixing Random Sequences

2014 ◽  
Vol 678 ◽  
pp. 112-115
Author(s):  
He Yu Li ◽  
Xi Li Tan
Keyword(s):  
Weak Convergence ◽  
Random Sequence ◽  
Moment Inequality ◽  
Random Sums ◽  
Random Sequences ◽  
Related Literature ◽  
Truncation Method ◽  
The Moment

Let {Xnk,n≥1,k≥1} be a ρ--mixing random sequence, by using the moment inequality and truncation method, we studied the weak convergence of random sums for ρ--mixing random sequence, which extended and improved some results in related literature.

Weak Convergence of Random Sums

2002 ◽  
Vol 46 (1) ◽  
pp. 39-57 ◽  
Author(s):  
V. M. Kruglov ◽  
Zhang Bo
Keyword(s):  
Weak Convergence ◽  
Random Sums

Common Fixed Points in Modular Spaces

2018 ◽  
pp. 502 ◽  
Author(s):  
Salwa Salman Abed ◽  
Karrar Emad Abdul Sada
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Fixed Point Theorems ◽  
Active Role ◽  
Common Fixed Points ◽  
Weakly Compact ◽  
Expansive Mapping ◽  
Modular Spaces ◽  
Opial’S Property ◽  
Common Fixed Point Theorems

     In this paper,there are   new considerations about the dual of a modular spaces and weak convergence. Two common fixed point theorems for a -non-expansive mapping defined on a star-shaped weakly compact subset are proved,  Here the conditions of affineness, demi-closedness and Opial's property play an active role in the proving our results.  

scholarly journals Weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain

2021 ◽  
Vol 58 (2) ◽  
pp. 372-393
Author(s):  
H. M. Jansen
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
The State ◽  
Stochastic Integrals ◽  
Occupation Measure ◽  
Generator Matrix ◽  
Markov Modulated ◽  
Erlang Loss

AbstractOur aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale, we provide sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure. We apply our results to derive diffusion limits for the Markov-modulated Erlang loss model and the regime-switching Cox–Ingersoll–Ross process.

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