scholarly journals The density of a passage time for a renewal-reward process perturbed by a diffusion

2013 ◽  
Vol 26 (1) ◽  
pp. 108-112 ◽  
Author(s):  
Christophette Blanchet-Scalliet ◽  
Diana Dorobantu ◽  
Didier Rullière
Keyword(s):  
Passage Time ◽  
Reward Process ◽  
Renewal Reward Process

Sample quantiles of additive renewal reward processes

1996 ◽  
Vol 33 (04) ◽  
pp. 1018-1032 ◽  
Author(s):  
Angelos Dassios
Keyword(s):  
Brownian Motion ◽  
Random Processes ◽  
Independent Increments ◽  
Look Back ◽  
Renewal Reward Processes ◽  
Reward Process ◽  
Renewal Reward Process ◽  
Sample Quantiles

The distribution of the sample quantiles of random processes is important for the pricing of some of the so-called financial ‘look-back' options. In this paper a representation of the distribution of the α-quantile of an additive renewal reward process is obtained as the sum of the supremum and the infimum of two rescaled independent copies of the process. This representation has already been proved for processes with stationary and independent increments. As an example, the distribution of the α-quantile of a randomly observed Brownian motion is obtained.

Policy Improvement and the Newton–Raphson Algorithm for Renewal Reward Processes

1989 ◽  
Vol 3 (3) ◽  
pp. 393-396 ◽  
Author(s):  
J. M. McNamara
Keyword(s):  
Continuous Time ◽  
Successive Approximations ◽  
Average Reward ◽  
Policy Improvement ◽  
Unique Root ◽  
Renewal Reward Processes ◽  
Reward Process ◽  
Newton Raphson ◽  
Renewal Reward Process ◽  
Raphson Algorithm

We consider a renewal reward process in continuous time. The supremum average reward, γ* for this process can be characterised as the unique root of a certain function. We show how one can apply the Newton–Raphson algorithm to obtain successive approximations to γ*, and show that the successive approximations so obtained are the same as those obtained by using the policy improvement technique.

Fuzzy random renewal process and renewal reward process

2007 ◽  
Vol 6 (3) ◽  
pp. 279-295 ◽  
Author(s):  
Ruiqing Zhao ◽  
Wansheng Tang ◽  
Cheng Wang
Keyword(s):  
Renewal Process ◽  
Reward Process ◽  
Renewal Reward Process ◽  
Fuzzy Random

scholarly journals A semi-Markovian renewal reward process withΓ(g)distributed demand

2020 ◽  
Vol 44 (4) ◽  
pp. 1250-1262
Author(s):  
Aslı BEKTAŞ KAMIŞLIK ◽  
Büşra ALAKOÇ ◽  
Tülay KESEMEN ◽  
Tahir KHANİYEV
Keyword(s):  
Reward Process ◽  
Renewal Reward Process

FLUCTUATIONS OF RENEWAL-REWARD PROCESS

1966 ◽  
Author(s):  
William S. Jewell
Keyword(s):  
Reward Process ◽  
Renewal Reward Process

Repair limit policy of aircraft component based on extended uncertain random renewal reward process

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chunxiao Zhang ◽  
Xinwang Li ◽  
Xiaona Liu ◽  
Qiang Li ◽  
Yizhou Bai
Keyword(s):  
Programming Model ◽  
Civil Aviation ◽  
Maintenance Cost ◽  
Engineering Practice ◽  
Content Type ◽  
Limit Time ◽  
Aircraft Component ◽  
New Type ◽  
Reward Process ◽  
Renewal Reward Process

PurposeThe purpose of this paper is to focus on an optimizing maintenance policy with repair limit time for a new type of aircraft component, in which the lifetime is assumed to be an uncertain variable due to no historical operation data, and the repair time is a random variable that can be described by the experimental data.Design/methodology/approachTo describe this repair limit time policy over an infinite time horizon, an extended uncertain random renewal reward theorem is firstly proposed based on chance theory, involves uncertain random interarrival times and stochastic rewards. Accordingly, the uncertain random programming model, which minimized the expected maintenance cost rate, is formulated to find the optimal repair limit time.FindingsA numerical example with sensitivity analysis is provided to illustrate the utility of the proposed policy. It provides a useful reference and guidance for aircraft optimization. For maintainers, it plays an important guiding role in engineering practice.Originality/valueThe proposed uncertain random renewal reward process proved useful for the optimization of maintenance strategy with maintenance limited time for a new type of aircraft components, which provides scientific support for aircraft maintenance decision-making for civil aviation enterprises.

Sample quantiles of additive renewal reward processes

1996 ◽  
Vol 33 (4) ◽  
pp. 1018-1032 ◽  
Author(s):  
Angelos Dassios
Keyword(s):  
Brownian Motion ◽  
Random Processes ◽  
Independent Increments ◽  
Look Back ◽  
Renewal Reward Processes ◽  
Reward Process ◽  
Renewal Reward Process ◽  
Sample Quantiles

The distribution of the sample quantiles of random processes is important for the pricing of some of the so-called financial ‘look-back' options. In this paper a representation of the distribution of the α-quantile of an additive renewal reward process is obtained as the sum of the supremum and the infimum of two rescaled independent copies of the process. This representation has already been proved for processes with stationary and independent increments. As an example, the distribution of the α-quantile of a randomly observed Brownian motion is obtained.

Perturbation theory for Markov reward processes with applications to queueing systems

1988 ◽  
Vol 20 (1) ◽  
pp. 79-98 ◽  
Author(s):  
Nico M. Van Dijk ◽  
Martin L. Puterman
Keyword(s):  
First Passage Time ◽  
Queueing Systems ◽  
Infinite Horizon ◽  
Passage Time ◽  
Decision Processes ◽  
Markov Decision ◽  
Reward Process ◽  
Reward Functions ◽  
Markov Reward ◽  
Time Bounds

We study the effect of perturbations in the data of a discrete-time Markov reward process on the finite-horizon total expected reward, the infinite-horizon expected discounted and average reward and the total expected reward up to a first-passage time. Bounds for the absolute errors of these reward functions are obtained. The results are illustrated for a finite as well as infinite queueing systems (M/M/1/S and ). Extensions to Markov decision processes and other settings are discussed.

A multivariate reward process defined on a semi-Markov process and its first-passage-time distributions

1991 ◽  
Vol 28 (2) ◽  
pp. 360-373 ◽  
Author(s):  
Yasushi Masuda ◽  
Ushio Sumita
Keyword(s):  
Asymptotic Behavior ◽  
Markov Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Renewal Equations ◽  
Supplementary Variables ◽  
Semi Markov Process ◽  
Reward Process

A multivariate reward process defined on a semi-Markov process is studied. Transform results for the distributions of the multivariate reward and related processes are derived through the method of supplementary variables and the Markov renewal equations. These transform results enable the asymptotic behavior to be analyzed. A class of first-passage time distributions of the multivariate reward processes is also investigated.

Sign in / Sign up

Export Citation Format

Share Document