Weak convergence of laws of stochastic processes on Riemannian manifolds

2001 ◽  
Vol 119 (4) ◽  
pp. 529-557 ◽  
Author(s):  
Yukio Ogura
Keyword(s):  
Weak Convergence ◽  
Stochastic Processes ◽  
Riemannian Manifolds

Weak Convergence to Stochastic Integrals

2021 ◽  
pp. 724-756
Author(s):  
James Davidson
Keyword(s):  
Brownian Motion ◽  
Weak Convergence ◽  
Stochastic Processes ◽  
Final Section ◽  
Stochastic Integrals ◽  
Martingale Difference ◽  
Mixing Processes ◽  
Linear Processes ◽  
Special Cases

The main object of this chapter is to prove the convergence of the covariances of stochastic processes with their increments to stochastic integrals with respect to Brownian motion. Some preliminary theory is given relating to random functionals on C, stochastic integrals, and the important Itô isometry. The main result is first proved for the tractable special cases of martingale difference increments and linear processes. The final section is devoted to proving the more difficult general case, of NED functions of mixing processes.

scholarly journals On the weak convergence of stochastic processes with embedded point processes

1988 ◽  
Vol 20 (2) ◽  
pp. 473-475 ◽  
Author(s):  
Panagiotis Konstantopoulos ◽  
Jean Walrand
Keyword(s):  
Stochastic Process ◽  
Weak Convergence ◽  
Stochastic Processes ◽  
Point Process ◽  
Real Line ◽  
Continuous Time ◽  
Point Processes ◽  
Mixing Condition ◽  
The Real ◽  
Palm Distribution

We consider a stochastic process in continuous time and two point processes on the real line, all jointly stationary. We show that under a certain mixing condition the values of the process at the points of the second point process converge weakly under the Palm distribution with respect to the first point process, and we identify the limit. This result is a supplement to two other known results which are mentioned below.

Some applications of weak convergence to statistics

1988 ◽  
Vol 25 (A) ◽  
pp. 201-211
Author(s):  
R. M. Loynes
Keyword(s):  
Weak Convergence ◽  
Stochastic Processes ◽  
Asymptotic Properties ◽  
Convergence Results

Results showing the weak convergence of certain stochastic processes are used to derive both known and new (asymptotic) properties of signs of residuals from regression; other weak convergence results are derived, and used to determine the behaviour of runs of residuals.

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.

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