scholarly journals On weak convergence of integral functionals of stochastic processes with applications to processes taking paths in LEP

1986 ◽  
Vol 21 (2) ◽  
pp. 305-317 ◽  
Author(s):  
Heinz Cremers ◽  
Dieter Kadelka
Keyword(s):  
Weak Convergence ◽  
Stochastic Processes ◽  
Integral Functionals

scholarly journals Perpetual integral functionals of multidimensional stochastic processes

Stochastics ◽  
2021 ◽  
pp. 1-12
Author(s):  
Yuri Kondratiev ◽  
Yuliya Mishura ◽  
José L. da Silva
Keyword(s):  
Stochastic Processes ◽  
Integral Functionals

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.

Asymptotic properties of integral functionals of geometric stochastic processes

2000 ◽  
Vol 37 (2) ◽  
pp. 480-493
Author(s):  
Endre Csáki ◽  
Miklós Csörgő ◽  
Antónia Földes ◽  
Pál Révész
Keyword(s):  
Stochastic Processes ◽  
Asymptotic Properties ◽  
Integral Functionals ◽  
Strong Invariance ◽  
Financial Modelling ◽  
Selection Of ◽  
General Conditions

We study strong asymptotic properties of two types of integral functionals of geometric stochastic processes. These integral functionals are of interest in financial modelling, yielding various option pricings, annuities, etc., by appropriate selection of the processes in their respective integrands. We show that under fairly general conditions on the latter processes the logs of the integral functionals themselves asymptotically behave like appropriate sup functionals of the processes in the exponents of their respective integrands. We illustrate the possible use and applications of these strong invariance theorems by listing and elaborating on several examples.

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.

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