scholarly journals Markov-modulated Ornstein–Uhlenbeck processes

2016 ◽  
Vol 48 (1) ◽  
pp. 235-254 ◽  
Author(s):  
G. Huang ◽  
H. M. Jansen ◽  
M. Mandjes ◽  
P. Spreij ◽  
K. De Turck
Keyword(s):  
Markov Process ◽  
Integration Theory ◽  
Background Process ◽  
Finite State ◽  
The Laplace Transform ◽  
Mean And Variance ◽  
The Mean ◽  
Markov Modulated ◽  
Set Up ◽  
Functional Central Limit

Abstract In this paper we consider an Ornstein–Uhlenbeck (OU) process (M(t))t≥0 whose parameters are determined by an external Markov process (X(t))t≥0 on a finite state space {1, . . ., d}; this process is usually referred to as Markov-modulated Ornstein–Uhlenbeck. We use stochastic integration theory to determine explicit expressions for the mean and variance of M(t). Then we establish a system of partial differential equations (PDEs) for the Laplace transform of M(t) and the state X(t) of the background process, jointly for time epochs t = t1, . . ., tK. Then we use this PDE to set up a recursion that yields all moments of M(t) and its stationary counterpart; we also find an expression for the covariance between M(t) and M(t + u). We then establish a functional central limit theorem for M(t) for the situation that certain parameters of the underlying OU processes are scaled, in combination with the modulating Markov process being accelerated; interestingly, specific scalings lead to drastically different limiting processes. We conclude the paper by considering the situation of a single Markov process modulating multiple OU processes.

Some renewal process models for single neuron discharge

1971 ◽  
Vol 8 (4) ◽  
pp. 802-808 ◽  
Author(s):  
Howard G. Hochman ◽  
Stephen E. Fienberg
Keyword(s):  
Single Neuron ◽  
Interspike Interval ◽  
Poisson Processes ◽  
Process Models ◽  
Recurrence Time ◽  
The Laplace Transform ◽  
Mean And Variance ◽  
The Mean ◽  
Interspike Interval Distribution ◽  
Interval Distribution

Leslie (1969) obtained the Laplace transform for the recurrence time of clusters of Poisson processes, which can be thought of as yielding the interspike interval distribution for a neuron that receives Poisson excitatory inputs subject to decay. Here, several extensions of this model are derived, each including Poisson inhibitory inputs. Expressions for the mean and variance are derived for each model, and the results for the different models are compared.

Fluid Model Driven by an M/M/1 Queue with Set-Up and Close-Down Period

2014 ◽  
Vol 513-517 ◽  
pp. 3377-3380
Author(s):  
Fu Wei Wang ◽  
Bing Wei Mao
Keyword(s):  
Stationary Distribution ◽  
Solution Method ◽  
Fluid Model ◽  
Model Driven ◽  
Buffer Content ◽  
The Laplace Transform ◽  
Matrix Geometric Solution ◽  
The Mean ◽  
Joint Stationary Distribution ◽  
Set Up

The fluid model driven by an M/M/1 queue with set-up and close-down period is studied. The Laplace transform of the joint stationary distribution of the fluid model is of matrix geometric structure. With matrix geometric solution method, the Laplace-Stieltjes transformation of the stationary distribution of the buffer content is obtained, as well as the mean buffer content. Finally, with some numerical examples, the effect of the parameters on mean buffer content is presented.

scholarly journals On Markov Modulated Mean-Reverting Price-Difference Models

2008 ◽  
Vol 13 ◽  
pp. 55
Author(s):  
W. P. Malcom ◽  
Lakhdar Aggoun ◽  
Mohamed Al-Lawati
Keyword(s):  
Stochastic Model ◽  
Markov Processes ◽  
Continuous Time ◽  
Price Difference ◽  
Time Dynamics ◽  
Price Process ◽  
Finite State ◽  
The Mean ◽  
New Feature ◽  
Markov Modulated

In this paper we develop a stochastic model incorporating a double-Markov modulated mean-reversion model. Unlike a price process the basis process X can take positive or negative values. This model is based on an explicit discretisation of the corresponding continuous time dynamics. The new feature in our model is that we suppose the mean reverting level in our dynamics as well as the noise coefficient can change according to the states of some finite-state Markov processes which could be the economy and some other unseen random phenomenon.  

Some renewal process models for single neuron discharge

1971 ◽  
Vol 8 (04) ◽  
pp. 802-808
Author(s):  
Howard G. Hochman ◽  
Stephen E. Fienberg
Keyword(s):  
Single Neuron ◽  
Interspike Interval ◽  
Poisson Processes ◽  
Process Models ◽  
Recurrence Time ◽  
The Laplace Transform ◽  
Mean And Variance ◽  
The Mean ◽  
Interspike Interval Distribution ◽  
Interval Distribution

Leslie (1969) obtained the Laplace transform for the recurrence time of clusters of Poisson processes, which can be thought of as yielding the interspike interval distribution for a neuron that receives Poisson excitatory inputs subject to decay. Here, several extensions of this model are derived, each including Poisson inhibitory inputs. Expressions for the mean and variance are derived for each model, and the results for the different models are compared.

Some renewal-theoretic investigations in the theory of sojourn times in finite semi-Markov processes

1991 ◽  
Vol 28 (04) ◽  
pp. 822-832 ◽  
Author(s):  
Attila Csenki
Keyword(s):  
Markov Process ◽  
Laplace Transform ◽  
Time Interval ◽  
Reliability Model ◽  
Finite State ◽  
The Laplace Transform ◽  
Semi Markov Process ◽  
Number Of Visits ◽  
Semi Markov Processes ◽  
Finite State Space

In this note, an irreducible semi-Markov process is considered whose finite state space is partitioned into two non-empty sets A and B. Let MB (t) stand for the number of visits of Y to B during the time interval [0, t], t > 0. A renewal argument is used to derive closed-form expressions for the Laplace transform (with respect to t) of a certain family of functions in terms of which the moments of MB (t) are easily expressible. The theory is applied to a small reliability model in conjunction with a Tauberian argument to evaluate the behaviour of the first two moments of MB (t) as t →∞.

scholarly journals ANALYSIS OF MARKOV-MODULATED INFINITE-SERVER QUEUES IN THE CENTRAL-LIMIT REGIME

2015 ◽  
Vol 29 (3) ◽  
pp. 433-459 ◽  
Author(s):  
Joke Blom ◽  
Koen De Turck ◽  
Michel Mandjes
Keyword(s):  
Central Limit ◽  
Background Process ◽  
Infinite Server ◽  
Deviation Matrix ◽  
Finite State ◽  
Transition Rate Matrix ◽  
Service Rates ◽  
Infinite Server Queues ◽  
Markov Modulated ◽  
Number Of Customers

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix Q≡(qij)i,j=1d. Both arrival rates and service rates are depending on the state of the background process. The main contribution concerns the derivation of central limit theorems (CLTs) for the number of customers in the system at time t≥0, in the asymptotic regime in which the arrival rates λi are scaled by a factor N, and the transition rates qij by a factor Nα, with α∈ℝ+. The specific value of α has a crucial impact on the result: (i) for α>1 the system essentially behaves as an M/M/∞ queue, and in the CLT the centered process has to be normalized by √N; (ii) for α<1, the centered process has to be normalized by N1−α/2, with the deviation matrix appearing in the expression for the variance.

Some renewal-theoretic investigations in the theory of sojourn times in finite semi-Markov processes

1991 ◽  
Vol 28 (4) ◽  
pp. 822-832 ◽  
Author(s):  
Attila Csenki
Keyword(s):  
Markov Process ◽  
Laplace Transform ◽  
Time Interval ◽  
Reliability Model ◽  
Finite State ◽  
The Laplace Transform ◽  
Semi Markov Process ◽  
Number Of Visits ◽  
Semi Markov Processes ◽  
Finite State Space

In this note, an irreducible semi-Markov process is considered whose finite state space is partitioned into two non-empty sets A and B. Let MB(t) stand for the number of visits of Y to B during the time interval [0, t], t > 0. A renewal argument is used to derive closed-form expressions for the Laplace transform (with respect to t) of a certain family of functions in terms of which the moments of MB(t) are easily expressible. The theory is applied to a small reliability model in conjunction with a Tauberian argument to evaluate the behaviour of the first two moments of MB(t) as t →∞.

scholarly journals Estimating the Mean Cover Time of a Semi-Markov Process via Simulation

1997 ◽  
Vol 11 (2) ◽  
pp. 267-271 ◽  
Author(s):  
Erol Peköz ◽  
Sheldon M. Ross
Keyword(s):  
Markov Process ◽  
Cover Time ◽  
Expected Time ◽  
Efficient Simulation ◽  
Finite State ◽  
Semi Markov Process ◽  
The Mean

An efficient simulation estimator of the expected time until all states of a finite state semi-Markov process have been visited is determined.

scholarly journals Weighted statistical binary patterns for facial feature representation

2021 ◽  
Author(s):  
Hung Phuoc Truong ◽  
Thanh Phuong Nguyen ◽  
Yong-Guk Kim
Keyword(s):  
Comprehensive Evaluation ◽  
Facial Feature ◽  
Input Image ◽  
Feature Representation ◽  
Illumination Variation ◽  
Straight Line ◽  
Mean And Variance ◽  
The Mean ◽  
Face Datasets ◽  
Degraded Images

AbstractWe present a novel framework for efficient and robust facial feature representation based upon Local Binary Pattern (LBP), called Weighted Statistical Binary Pattern, wherein the descriptors utilize the straight-line topology along with different directions. The input image is initially divided into mean and variance moments. A new variance moment, which contains distinctive facial features, is prepared by extracting root k-th. Then, when Sign and Magnitude components along four different directions using the mean moment are constructed, a weighting approach according to the new variance is applied to each component. Finally, the weighted histograms of Sign and Magnitude components are concatenated to build a novel histogram of Complementary LBP along with different directions. A comprehensive evaluation using six public face datasets suggests that the present framework outperforms the state-of-the-art methods and achieves 98.51% for ORL, 98.72% for YALE, 98.83% for Caltech, 99.52% for AR, 94.78% for FERET, and 99.07% for KDEF in terms of accuracy, respectively. The influence of color spaces and the issue of degraded images are also analyzed with our descriptors. Such a result with theoretical underpinning confirms that our descriptors are robust against noise, illumination variation, diverse facial expressions, and head poses.

scholarly journals Groups and Individuals: Optical Flow Patterns of Broiler Chicken Flocks Are Correlated with the Behavior of Individual Birds

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 568
Author(s):  
Sabine G. Gebhardt-Henrich ◽  
Ariane Stratmann ◽  
Marian Stamp Dawkins
Keyword(s):  
Optical Flow ◽  
Broiler Chicken ◽  
Average Length ◽  
Flow Patterns ◽  
Group Level ◽  
Positive Correlation ◽  
Water Test ◽  
Mean And Variance ◽  
The Mean

Group level measures of welfare flocks have been criticized on the grounds that they give only average measures and overlook the welfare of individual animals. However, we here show that the group-level optical flow patterns made by broiler flocks can be used to deliver information not just about the flock averages but also about the proportion of individuals in different movement categories. Mean optical flow provides information about the average movement of the whole flock while the variance, skew and kurtosis quantify the variation between individuals. We correlated flock optical flow patterns with the behavior and welfare of a sample of 16 birds per flock in two runway tests and a water (latency-to-lie) test. In the runway tests, there was a positive correlation between the average time taken to complete the runway and the skew and kurtosis of optical flow on day 28 of flock life (on average slow individuals came from flocks with a high skew and kurtosis). In the water test, there was a positive correlation between the average length of time the birds remained standing and the mean and variance of flock optical flow (on average, the most mobile individuals came from flocks with the highest mean). Patterns at the flock level thus contain valuable information about the activity of different proportions of the individuals within a flock.

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