The Number of Visits to a Subset of the State Space by a Continuous-Parameter Irreducible Markov Chain During a Finite Time Interval

1994 ◽  
pp. 106-121
Author(s):  
Attila Csenki
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Finite Time ◽  
The State ◽  
Time Interval ◽  
Finite Time Interval ◽  
Continuous Parameter ◽  
Number Of Visits ◽  
Irreducible Markov Chain

A method for approximating the probability functions of a Markov chain

1988 ◽  
Vol 25 (4) ◽  
pp. 808-814 ◽  
Author(s):  
Keith N. Crank
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Finite Number ◽  
Continuous Time ◽  
Finite Time ◽  
The State ◽  
Time Interval ◽  
Continuous Time Markov Chain ◽  
Finite Time Interval ◽  
System Of Differential Equations

This paper presents a method of approximating the state probabilities for a continuous-time Markov chain. This is done by constructing a right-shift process and then solving the Kolmogorov system of differential equations recursively. By solving a finite number of the differential equations, it is possible to obtain the state probabilities to any degree of accuracy over any finite time interval.

A method for approximating the probability functions of a Markov chain

1988 ◽  
Vol 25 (04) ◽  
pp. 808-814 ◽  
Author(s):  
Keith N. Crank
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Finite Number ◽  
Continuous Time ◽  
Finite Time ◽  
The State ◽  
Time Interval ◽  
Continuous Time Markov Chain ◽  
Finite Time Interval ◽  
System Of Differential Equations

This paper presents a method of approximating the state probabilities for a continuous-time Markov chain. This is done by constructing a right-shift process and then solving the Kolmogorov system of differential equations recursively. By solving a finite number of the differential equations, it is possible to obtain the state probabilities to any degree of accuracy over any finite time interval.

scholarly journals Finite-Time Boundedness for a Class of Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li Liang
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
The State ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markovian Jumping ◽  
Stochastic Boundedness ◽  
Partly Unknown Transition Probabilities ◽  
Finite Time Boundedness

This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results.

scholarly journals Finite-Time H2/H∞ Control Design for Stochastic Poisson Systems with Applications to Clothing Hanging Device

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yan Qi ◽  
Shiyu Zhong ◽  
Zhiguo Yan
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Control Design ◽  
The State ◽  
Time Interval ◽  
Finite Time Interval ◽  
Transient Performance ◽  
Definition Of

In this paper, the design of finite-time H2/H∞ controller for linear Itô stochastic Poisson systems is considered. First, the definition of finite-time H2/H∞ control is proposed, which considers the transient performance, H2 index, and H∞ index simultaneously in a predetermined finite-time interval. Then, the state feedback and observer-based finite-time H2/H∞ controllers are presented and some new sufficient conditions are obtained. Moreover, an algorithm is given to optimize H2 and H∞ index, simultaneously. Finally, a simulation example indicates the effectiveness of the results.

scholarly journals Markov Chains Conditioned Never to Wait Too Long at the Origin

2009 ◽  
Vol 46 (03) ◽  
pp. 812-826
Author(s):  
Saul Jacka
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Sufficient Conditions ◽  
Weak Limit ◽  
The State ◽  
Coin Tossing ◽  
First Time ◽  
Vague Convergence ◽  
Irreducible Markov Chain

Motivated by Feller's coin-tossing problem, we consider the problem of conditioning an irreducible Markov chain never to wait too long at 0. Denoting by τ the first time that the chain,X, waits for at least one unit of time at the origin, we consider conditioning the chain on the event (τ›T). We show that there is a weak limit asT→∞ in the cases where either the state space is finite orXis transient. We give sufficient conditions for the existence of a weak limit in other cases and show that we have vague convergence to a defective limit if the time to hit zero has a lighter tail than τ and τ is subexponential.

scholarly journals Exact simulation of the extrema of stable processes

2019 ◽  
Vol 51 (4) ◽  
pp. 967-993
Author(s):  
Jorge I. González Cázares ◽  
Aleksandar Mijatović ◽  
Gerónimo Uribe Bravo
Keyword(s):  
Markov Chain ◽  
Finite Time ◽  
Stable Process ◽  
Stable Processes ◽  
Time Interval ◽  
Simulation Algorithm ◽  
Finite Time Interval ◽  
Exact Simulation ◽  
The Past ◽  
Coupling From The Past

AbstractWe exhibit an exact simulation algorithm for the supremum of a stable process over a finite time interval using dominated coupling from the past (DCFTP). We establish a novel perpetuity equation for the supremum (via the representation of the concave majorants of Lévy processes [27]) and use it to construct a Markov chain in the DCFTP algorithm. We prove that the number of steps taken backwards in time before the coalescence is detected is finite. We analyse the performance of the algorithm numerically (the code, written in Julia 1.0, is available on GitHub).

scholarly journals Markov Chains Conditioned Never to Wait Too Long at the Origin

2009 ◽  
Vol 46 (3) ◽  
pp. 812-826
Author(s):  
Saul Jacka
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Sufficient Conditions ◽  
Weak Limit ◽  
The State ◽  
Coin Tossing ◽  
First Time ◽  
Vague Convergence ◽  
Irreducible Markov Chain

Motivated by Feller's coin-tossing problem, we consider the problem of conditioning an irreducible Markov chain never to wait too long at 0. Denoting by τ the first time that the chain, X, waits for at least one unit of time at the origin, we consider conditioning the chain on the event (τ›T). We show that there is a weak limit as T→∞ in the cases where either the state space is finite or X is transient. We give sufficient conditions for the existence of a weak limit in other cases and show that we have vague convergence to a defective limit if the time to hit zero has a lighter tail than τ and τ is subexponential.

Sign in / Sign up

Export Citation Format

Share Document