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.

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.

Malthusian behaviour of the critical and subcritical age-dependent branching processes with arbitrary state space

1976 ◽  
Vol 13 (3) ◽  
pp. 455-465
Author(s):  
D. I. Saunders
Keyword(s):  
State Space ◽  
Branching Process ◽  
Branching Processes ◽  
Rates Of Convergence ◽  
Expected Number ◽  
Subcritical Case ◽  
Arbitrary State ◽  
Malthusian Parameter ◽  
Age Dependent ◽  
Number Of Individuals

For the age-dependent branching process with arbitrary state space let M(x, t, A) be the expected number of individuals alive at time t with states in A given an initial individual at x. Subject to various conditions it is shown that M(x, t, A)e–at converges to a non-trivial limit where α is the Malthusian parameter (α = 0 for the critical case, and is negative in the subcritical case). The method of proof also yields rates of convergence.

Simulated annealing process in general state space

1991 ◽  
Vol 23 (04) ◽  
pp. 866-893 ◽  
Author(s):  
Heikki Haario ◽  
Eero Saksman
Keyword(s):  
Stochastic Process ◽  
Simulated Annealing ◽  
State Space ◽  
Annealing Process ◽  
General State ◽  
Arbitrary State ◽  
Strong And Weak Convergence ◽  
General State Space ◽  
Rate Of Cooling ◽  
Space Conditions

The stochastic process corresponding to the simulated annealing optimization algorithm is generalized to the case of an arbitrary state space. Conditions for the strong and weak convergence of the process are established. In addition the relation between the size of the generating distributions and the possible rate of cooling is studied.

Phase Space Reconstruction

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Dynamical Systems ◽  
Statistical Mechanics ◽  
State Space ◽  
Phase Plane ◽  
Material Point ◽  
The Other ◽  
Straight Line ◽  
Mathematical Construction

In this chapter we introduce an important concept concerning the study of both discrete and continuous dynamical systems, the concept of phase space or “state space”. It is an abstract mathematical construction with important applications in statistical mechanics, to represent the time evolution of a dynamical system in geometric shape. This space has as many dimensions as the number of variables needed to define the instantaneous state of the system. For instance, the state of a material point moving on a straight line is defined by its position and velocity at each instant, so that the phase space for this system is a plane in which one axis is the position and the other one the velocity. In this case, the phase space is also called “phase plane”. It is later applied in many chapters of the book.

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