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.

Discretizations for the average impulse control of piecewise deterministic processes

1993 ◽  
Vol 30 (02) ◽  
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.

scholarly journals Thinning and multilevel Monte Carlo methods for piecewise deterministic (Markov) processes with an application to a stochastic Morris–Lecar model

2020 ◽  
Vol 52 (1) ◽  
pp. 138-172
Author(s):  
Vincent Lemaire ◽  
MichÉle Thieullen ◽  
Nicolas Thomas
Keyword(s):  
Monte Carlo ◽  
Markov Processes ◽  
Building Blocks ◽  
Not Given ◽  
Multilevel Monte Carlo ◽  
The Third ◽  
Piecewise Deterministic Markov Processes ◽  
Deterministic Processes ◽  
Piecewise Deterministic Processes ◽  
Weak Error

AbstractIn the first part of this paper we study approximations of trajectories of piecewise deterministic processes (PDPs) when the flow is not given explicitly by the thinning method. We also establish a strong error estimate for PDPs as well as a weak error expansion for piecewise deterministic Markov processes (PDMPs). These estimates are the building blocks of the multilevel Monte Carlo (MLMC) method, which we study in the second part. The coupling required by the MLMC is based on the thinning procedure. In the third part we apply these results to a two-dimensional Morris–Lecar model with stochastic ion channels. In the range of our simulations the MLMC estimator outperforms classical Monte Carlo.

Piecewise deterministic processes following two alternating patterns

2019 ◽  
Vol 56 (4) ◽  
pp. 1006-1019 ◽  
Author(s):  
Nikita Ratanov ◽  
Antonio Di Crescenzo ◽  
Barbara Martinucci
Keyword(s):  
State Space ◽  
Arbitrary State ◽  
Telegraph Process ◽  
Straight Line ◽  
Deterministic Processes ◽  
Piecewise Deterministic Processes

AbstractWe propose a wide generalization of known results related to the telegraph process. Functionals of the simple telegraph process on a straight line and their generalizations on an arbitrary state space are studied.

scholarly journals Viscosity solutions associated with impulse control problems for piecewise-deterministic processes

1989 ◽  
Vol 12 (1) ◽  
pp. 145-157 ◽  
Author(s):  
Suzanne M. Lenhart
Keyword(s):  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Impulse Control ◽  
Control Problems ◽  
Bounded Domains ◽  
Existence And Uniqueness Results ◽  
Impulse Control Problem ◽  
Uniqueness Results ◽  
Deterministic Processes ◽  
Piecewise Deterministic Processes

This paper considers existence and uniqueness results for viscosity solutions of integro-differential equations associated with the impulse control problem for piecewise-deterministic processes on bounded domains and on Rn.

scholarly journals Optimal strategies for impulse control of piecewise deterministic Markov processes

Automatica ◽  
2017 ◽  
Vol 77 ◽  
pp. 219-229 ◽  
Author(s):  
Benoîte de Saporta ◽  
François Dufour ◽  
Alizée Geeraert
Keyword(s):  
Markov Processes ◽  
Impulse Control ◽  
Optimal Strategies ◽  
Piecewise Deterministic Markov Processes
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