scholarly journals A Non-Skorohod Topology on the Skorohod Space

1997 ◽  
Vol 2 (0) ◽  
Author(s):  
Adam Jakubowski
Keyword(s):  
Skorohod Topology ◽  
Skorohod Space

Point processes and random measures

1977 ◽  
Vol 9 (3) ◽  
pp. 502-526 ◽  
Author(s):  
Jan Grandell
Keyword(s):  
Point Processes ◽  
Probability Measures ◽  
Simple Point ◽  
Topological Properties ◽  
Random Measures ◽  
Short Introduction ◽  
Convergence Of Probability Measures ◽  
Skorohod Topology

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.

Point processes and random measures

1977 ◽  
Vol 9 (03) ◽  
pp. 502-526 ◽  
Author(s):  
Jan Grandell
Keyword(s):  
Point Processes ◽  
Probability Measures ◽  
Simple Point ◽  
Topological Properties ◽  
Random Measures ◽  
Short Introduction ◽  
Convergence Of Probability Measures ◽  
Skorohod Topology

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.

On Lévy’s Equivalence Theorem in Skorohod Space

2013 ◽  
pp. 219-225
Author(s):  
Andreas Basse-O’Connor ◽  
Jan Rosiński
Keyword(s):  
Equivalence Theorem ◽  
Skorohod Space

WEAK CONVERGENCE TO LÉVY STABLE PROCESSES IN DYNAMICAL SYSTEMS

2010 ◽  
Vol 10 (02) ◽  
pp. 263-289 ◽  
Author(s):  
MARTA TYRAN-KAMIŃSKA
Keyword(s):  
Dynamical Systems ◽  
Weak Convergence ◽  
Stable Process ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stable Processes ◽  
Skorohod Space ◽  
Necessary And Sufficient

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.

scholarly journals Modelling and Regularity of Nonlinear Impulsive Switching Dynamical System in Fed-Batch Culture

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Lei Wang
Keyword(s):  
Batch Culture ◽  
Computational Cost ◽  
Specific Form ◽  
Essential Difference ◽  
Switching System ◽  
Fed Batch ◽  
Batch Production ◽  
Impulsive Event ◽  
Skorohod Topology ◽  
Fed Batch Culture

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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