scholarly journals A Non-Skorohod Topology on the Skorohod Space

1997 ◽  
Vol 2 (0) ◽  
Author(s):  
Adam Jakubowski
1977 ◽  
Vol 9 (3) ◽  
pp. 502-526 ◽  
Author(s):  
Jan Grandell

The purpose of this paper is to give a short introduction to the theory of point processes and random measures. Our hope is that the paper can be used as a complement to a study of Billingsley's book Convergence of Probability Measures. The subjects treated are: topological properties of the space of realizations; characterization and convergence of random measures with special attention to simple point processses and diffuse random measures; the relation between the topology used and the Skorohod topology. Some thinning and superposition results are given without proofs.


1977 ◽  
Vol 9 (03) ◽  
pp. 502-526 ◽  
Author(s):  
Jan Grandell

The purpose of this paper is to give a short introduction to the theory of point processes and random measures. Our hope is that the paper can be used as a complement to a study of Billingsley's book Convergence of Probability Measures. The subjects treated are: topological properties of the space of realizations; characterization and convergence of random measures with special attention to simple point processses and diffuse random measures; the relation between the topology used and the Skorohod topology. Some thinning and superposition results are given without proofs.


2013 ◽  
pp. 219-225
Author(s):  
Andreas Basse-O’Connor ◽  
Jan Rosiński

2010 ◽  
Vol 10 (02) ◽  
pp. 263-289 ◽  
Author(s):  
MARTA TYRAN-KAMIŃSKA

We study convergence of normalized ergodic sum processes to Lévy stable process in the Skorohod space with J1-topology. Our necessary and sufficient conditions allow us to prove or disprove such convergence for specific examples.


2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Lei Wang

A hybrid system with state-based switchings is proposed to describe the fed-batch production of 1,3-propandiol from glycerol in our previous work. However, the on-off switching of alkali is too frequent, which greatly increases the computational cost of the numerical solution to the system so as to locate the state-based switchings in strict time order and implement the correct mode changes. To deal with this problem, we consider the switching of alkali pump as an impulsive event and present a nonlinear impulsive switching system to describe the fed-batch culture. It is proved that the impulsive switching system is non-Zeno. Some basic properties of solutions to the impulsive switching system are also explored. In order to overcome the discontinuities of the system, the Skorohod topology is induced and a specific form ofλis constructed to prove the main theorem. Additionally, a numerical simulation is carried out to show that the proposed system can describe the fed-batch culture properly and the essential difference with the previous work.


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