Extension of the results of Chapters 3 and 4 to generalized renewal processes

2010 ◽  
pp. 543-601
Author(s):  
A. A. Borovkov ◽  
K. A. Borovkov
Keyword(s):  
Renewal Processes

scholarly journals Simulating the effects of redesigned street-scale built environments on access/egress pedestrian flows to metro stations

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Yanan Liu ◽  
Dujuan Yang ◽  
Harry J. P. Timmermans ◽  
Bauke de Vries
Keyword(s):  
Built Environment ◽  
Route Choice ◽  
Local Area ◽  
Destination Choice ◽  
Built Environments ◽  
Renewal Processes ◽  
City Center ◽  
Metro Station ◽  
Route Choice Behavior ◽  
The City

AbstractIn urban renewal processes, metro line systems are widely used to accommodate the massive traffic needs and stimulate the redevelopment of the local area. The route choice of pedestrians, emanating from or going to the metro stations, is influenced by the street-scale built environment. Many renewal processes involve the improvement of the street-level built environment and thus influence pedestrian flows. To assess the effects of urban design on pedestrian flows, this article presents the results of a simulation model of pedestrian route choice behavior around Yingkoudao metro station in the city center of Tianjin, China. Simulated pedestrian flows based on 4 scenarios of changes in street-scale built environment characteristics are compared. Results indicate that the main streets are disproportionally more affected than smaller streets. The promotion of an intensified land use mix does not lead to a high increase in the number of pedestrians who choose the involved route when traveling from/to the metro station, assuming fixed destination choice.

scholarly journals Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 55
Author(s):  
P.-C.G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Renewal Process ◽  
Markov Chain Model ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Chain Model ◽  
Markov Renewal Processes ◽  
Risky Bonds ◽  
Markov Structure

For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.

scholarly journals Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 905
Author(s):  
Nina Megier ◽  
Manuel Ponzi ◽  
Andrea Smirne ◽  
Bassano Vacchini
Keyword(s):  
Quantum Dynamics ◽  
Open Quantum System ◽  
Open Quantum Systems ◽  
Phenomenological Approach ◽  
Quantum Systems ◽  
Renewal Processes ◽  
Continuous Part ◽  
Trace Distance ◽  
Open Quantum ◽  
And Control

Simple, controllable models play an important role in learning how to manipulate and control quantum resources. We focus here on quantum non-Markovianity and model the evolution of open quantum systems by quantum renewal processes. This class of quantum dynamics provides us with a phenomenological approach to characterise dynamics with a variety of non-Markovian behaviours, here described in terms of the trace distance between two reduced states. By adopting a trajectory picture for the open quantum system evolution, we analyse how non-Markovianity is influenced by the constituents defining the quantum renewal process, namely the time-continuous part of the dynamics, the type of jumps and the waiting time distributions. We focus not only on the mere value of the non-Markovianity measure, but also on how different features of the trace distance evolution are altered, including times and number of revivals.

scholarly journals Quantum renewal processes

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Bassano Vacchini
Keyword(s):  
Renewal Processes

Stochastic impulsive processes on a superposition of two renewal processes

2015 ◽  
Vol 206 (1) ◽  
pp. 58-68
Author(s):  
Vladimir S. Koroliuk ◽  
Raimondo Manca ◽  
Guglielmo D’Amico
Keyword(s):  
Renewal Processes ◽  
Impulsive Processes

Filtering of Markov renewal queues, IV: Flow processes in feedback queues

1985 ◽  
Vol 17 (2) ◽  
pp. 386-407 ◽  
Author(s):  
Jeffrey J. Hunter
Keyword(s):  
Queue Length ◽  
Queueing Systems ◽  
Arrival Process ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Flow Process ◽  
Special Cases ◽  
Flow Processes ◽  
Transition Points ◽  
The Times

This paper is a continuation of the study of a class of queueing systems where the queue-length process embedded at basic transition points, which consist of ‘arrivals’, ‘departures’ and ‘feedbacks’, is a Markov renewal process (MRP). The filtering procedure of Çinlar (1969) was used in [12] to show that the queue length process embedded separately at ‘arrivals’, ‘departures’, ‘feedbacks’, ‘inputs’ (arrivals and feedbacks), ‘outputs’ (departures and feedbacks) and ‘external’ transitions (arrivals and departures) are also MRP. In this paper expressions for the elements of each Markov renewal kernel are derived, and thence expressions for the distribution of the times between transitions, under stationary conditions, are found for each of the above flow processes. In particular, it is shown that the inter-event distributions for the arrival process and the departure process are the same, with an equivalent result holding for inputs and outputs. Further, expressions for the stationary joint distributions of successive intervals between events in each flow process are derived and interconnections, using the concept of reversed Markov renewal processes, are explored. Conditions under which any of the flow processes are renewal processes or, more particularly, Poisson processes are also investigated. Special cases including, in particular, the M/M/1/N and M/M/1 model with instantaneous Bernoulli feedback, are examined.

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

scholarly journals A Large Sample Test for the Independence of Two Renewal Processes

1967 ◽  
Vol 38 (4) ◽  
pp. 1037-1041
Author(s):  
Sidney C. Port ◽  
Charles J. Stone
Keyword(s):  
Renewal Processes ◽  
Large Sample ◽  
Sample Test

Superimposed renewal processes

1985 ◽  
Vol 111 (7) ◽  
pp. 359-362
Author(s):  
G Faraci ◽  
A.R Pennisi
Keyword(s):  
Renewal Processes
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