scholarly journals Deriving a kinetic uncertainty relation for piecewise deterministic processes: from classical to quantum

2021 ◽  
Author(s):  
Fei Liu
Keyword(s):  
Uncertainty Relation ◽  
Deterministic Processes ◽  
Piecewise Deterministic Processes

Discretizations for the average impulse control of piecewise deterministic processes

1993 ◽  
Vol 30 (2) ◽  
pp. 405-420 ◽  
Author(s):  
O. L. V. Costa
Keyword(s):  
State Space ◽  
Markov Processes ◽  
Impulse Control ◽  
Time Discretization ◽  
Optimal Capacity ◽  
Piecewise Deterministic Markov Processes ◽  
Deterministic Processes ◽  
General Average ◽  
Piecewise Deterministic Processes ◽  
Discretized Problem

This paper presents a state space and time discretization for the general average impulse control of piecewise deterministic Markov processes (PDPs). By combining several previous results we show that under some continuity, boundedness and compactness conditions on the parameters of the process, boundedness of the discretizations, and compactness of the state space, the discretized problem will converge uniformly to the original one. An application to optimal capacity expansion under uncertainty is given.

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