Extremal Tests for Weak Convergence of Sequences and Series

1984 ◽  
pp. 147-172
Author(s):  
Joseph Diestel
Keyword(s):  
Weak Convergence ◽  
Convergence Of Sequences

Weak convergence of sequences of semimartingales with applications to multitype branching processes

1986 ◽  
Vol 18 (1) ◽  
pp. 20-65 ◽  
Author(s):  
A. Joffe ◽  
M. Metivier
Keyword(s):  
Weak Convergence ◽  
Stochastic Processes ◽  
Special Class ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Convergence Of Sequences ◽  
Multitype Branching Processes

The paper is devoted to a systematic discussion of recently developed techniques for the study of weak convergence of sequences of stochastic processes. The methods described make essential use of the semimartingale structure of the processes. Sufficient conditions for tightness including the results of Rebolledo are derived. The techniques are applied to a special class of processes, namely the D-semimartingales. Applications to multitype branching processes are given.

Weak convergence of sequences of semimartingales with applications to multitype branching processes

1986 ◽  
Vol 18 (01) ◽  
pp. 20-65 ◽  
Author(s):  
A. Joffe ◽  
M. Metivier
Keyword(s):  
Weak Convergence ◽  
Stochastic Processes ◽  
Special Class ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Convergence Of Sequences ◽  
Multitype Branching Processes

The paper is devoted to a systematic discussion of recently developed techniques for the study of weak convergence of sequences of stochastic processes. The methods described make essential use of the semimartingale structure of the processes. Sufficient conditions for tightness including the results of Rebolledo are derived. The techniques are applied to a special class of processes, namely the D-semimartingales. Applications to multitype branching processes are given.

Weak convergence of sequences of random elements with random indices

1980 ◽  
Vol 88 (1) ◽  
pp. 171-174 ◽  
Author(s):  
M. Csörgő ◽  
Z. Rychlik
Keyword(s):  
Positive Integer ◽  
Weak Convergence ◽  
Metric Space ◽  
Probability Space ◽  
Random Element ◽  
Random Variables ◽  
Random Elements ◽  
Convergence Of Sequences ◽  
Random Indices ◽  
Separable Metric Space

Let (S, d) be a separable metric space equipped with its Borel σ field . Let {Yn, n ≥ 1} be a sequence of S-valued random elements defined on a probability space (Ω, , p). Assume Yn ⇒ Y converges weakly to an S-valued random element Y. Let {Nn, n ≥ 1} be a sequence of positive integer-valued random variables defined on the same probability space (Ω, , p).

On the weak convergence of sequences of circuit processes: a probabilistic approach

1992 ◽  
Vol 29 (02) ◽  
pp. 374-383 ◽  
Author(s):  
Sophia Kalpazidou
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Asymptotic Behaviour ◽  
Markov Processes ◽  
Probabilistic Approach ◽  
Probabilistic Interpretation ◽  
Sample Paths ◽  
Convergence Of Sequences ◽  
Recurrent Markov Chain ◽  
Positive Recurrent

The asymptotic behaviour of sequences of Markov processes whose finite distributions depend upon the sample paths ω of a positive recurrent Markov chain ξ is studied. The existence of such sequences depends upon the existence of a unique class of directed weighted circuits having a probabilistic interpretation in terms of the directed circuits occurring along the sample paths of ξ. An application to multiple Markov chains is given.

scholarly journals Weak convergence of sequences in function spaces

1969 ◽  
Vol 4 (3) ◽  
pp. 457-466 ◽  
Author(s):  
J.W Brace ◽  
G.D Friend
Keyword(s):  
Weak Convergence ◽  
Function Spaces ◽  
Convergence Of Sequences

scholarly journals On the Mikusiński-Antosik diagonal theorem and the equivalence of two types of convergence in Köthe spaces

2017 ◽  
Vol 101 (115) ◽  
pp. 151-160
Author(s):  
Andrzej Kamiński ◽  
Sławomir Sorek
Keyword(s):  
Weak Convergence ◽  
Simple Proof ◽  
Extended Form ◽  
Strong And Weak Convergence ◽  
Köthe Spaces ◽  
Convergence Of Sequences

We present a simple proof of the Mikusi?ski-Antosik diagonal theorem and apply this result to prove, in an extended form, the theorem on the equivalence of the strong and weak boundedness of sets and, consequently, of the strong and weak convergence of sequences in Kothe spaces.

scholarly journals On weak convergence of sequences of measures

1980 ◽  
Vol 6 (1) ◽  
pp. 65-72
Author(s):  
Harald Bergström
Keyword(s):  
Weak Convergence ◽  
Convergence Of Sequences
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