scholarly journals On the Location of the Maximum of a Continuous Stochastic Process

2014 ◽  
Vol 51 (01) ◽  
pp. 152-161 ◽  
Author(s):  
Leandro P. R. Pimentel
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Stationary Process ◽  
Mean Value ◽  
Necessary Condition ◽  
Linear Perturbation ◽  
Short Article ◽  
Underlying Process ◽  
The Mean ◽  
Sufficient And Necessary Condition

In this short article we will provide a sufficient and necessary condition to have uniqueness of the location of the maximum of a stochastic process over an interval. The result will also express the mean value of the location in terms of the derivative of the expectation of the maximum of a linear perturbation of the underlying process. As an application, we will consider a Brownian motion with variable drift. The ideas behind the method of proof will also be useful to study the location of the maximum, over the real line, of a two-sided Brownian motion minus a parabola and of a stationary process minus a parabola.

scholarly journals On the Location of the Maximum of a Continuous Stochastic Process

2014 ◽  
Vol 51 (1) ◽  
pp. 152-161 ◽  
Author(s):  
Leandro P. R. Pimentel
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Stationary Process ◽  
Mean Value ◽  
Necessary Condition ◽  
Linear Perturbation ◽  
Short Article ◽  
Underlying Process ◽  
The Mean ◽  
Sufficient And Necessary Condition

In this short article we will provide a sufficient and necessary condition to have uniqueness of the location of the maximum of a stochastic process over an interval. The result will also express the mean value of the location in terms of the derivative of the expectation of the maximum of a linear perturbation of the underlying process. As an application, we will consider a Brownian motion with variable drift. The ideas behind the method of proof will also be useful to study the location of the maximum, over the real line, of a two-sided Brownian motion minus a parabola and of a stationary process minus a parabola.

scholarly journals Perturbation analysis of a variable M/M/1 queue: a probabilistic approach

2006 ◽  
Vol 38 (01) ◽  
pp. 263-283 ◽  
Author(s):  
Nelson Antunes ◽  
Christine Fricker ◽  
Fabrice Guillemin ◽  
Philippe Robert
Keyword(s):  
Power Series ◽  
Busy Period ◽  
Stationary Process ◽  
Probabilistic Approach ◽  
Power Series Expansion ◽  
Mean Value ◽  
Service Rate ◽  
The Mean ◽  
The Impact ◽  
Period Duration

In this paper, motivated by the problem of the coexistence on transmission links of telecommunications networks of elastic and unresponsive traffic, we study the impact on the busy period of an M/M/1 queue of a small perturbation in the service rate. The perturbation depends upon an independent stationary process (X(t)) and is quantified by means of a parameter ε ≪ 1. We specifically compute the two first terms of the power series expansion in ε of the mean value of the busy period duration. This allows us to study the validity of the reduced service rate approximation, which consists in comparing the perturbed M/M/1 queue with the M/M/1 queue whose service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of the environment process (X(t)) play a key role.

scholarly journals UPAYA MENINGKATKAN PEMAHAMAN KONSEP SISWA PADA MATA PELAJARAN MATEMATIKA MELALUI MODEL PROBLEM POSING PADA SISWA DI SEKOLAH DASAR

2018 ◽  
Vol 2 (2) ◽  
pp. 155
Author(s):  
Arrahim Arrahim ◽  
Amelia Nur Fatimah
Keyword(s):  
Model Problem ◽  
Mean Value ◽  
Male Students ◽  
Problem Posing ◽  
Necessary Condition ◽  
Observation Data ◽  
Mathematics Students ◽  
Average Value ◽  
The Mean ◽  
Quantitative Descriptive

This research is motivated by the lack of understanding the concept of students in teaching math. This is evident from the students have not been able to explain the return of the material provided by the teacher, classify an object of such material in accordance with the properties that exist on the material, providing an example of what has been described, presents a picture that relates to the material, students are still difficulties in explains the necessary condition on the content being taught, to solve problems by using the steps correctly, solving the problem solving has been explained by the teacher. The purpose of this study is to improve students' understanding of concepts through learning model Problem Posing in Class VI SDI-Huda AL East Bekasi.Type of this research is the Classroom Action Research (PTK) and lasts for two cycles. Each cycle consisted of four meetings, with the stages of planning, implementation, observation, and reflection. Subjects in this study were students of class VI SDI-Huda AL East Bekasi with the number of students 23 students consisting of 9 male students and 14 female students. The data were obtained by tess and observation. Data were analyzed by descriptive qualitative and quantitative descriptive. The criteria for this research kerberhasilan is when 80% of the number of students reaching the KKM is 75.From the results obtained by the average value of the ability of understanding the concept of students in the first cycle of 75.28 with a percentage of 60.87% success. then in the second cycle The mean value of understanding the concept of students' ability to increase to 90.11 and 86.96% success rate. This shows that there is an increased understanding of the concept of the student after the model of Problem Posing. It can be concluded that the use of the model can be meningkatlkan Problem Posing student conceptual understanding in mathematics students of class VI SDI-Huda AL East Bekasi.

Excursions above a fixed level by n-dimensional random fields

1976 ◽  
Vol 13 (2) ◽  
pp. 276-289 ◽  
Author(s):  
Robert J. Adler
Keyword(s):  
Stochastic Process ◽  
Random Field ◽  
Random Fields ◽  
Mean Value ◽  
Regularity Conditions ◽  
Gaussian Field ◽  
Differential Topology ◽  
One Dimensional ◽  
Excursion Set ◽  
The Mean

For an n-dimensional random field X(t) we define the excursion set A of X(t) by A = [t ∊ S: X(t) ≧ u] for real u and compact S ⊂ Rn. We obtain a generalisation of the number of upcrossings of a one-dimensional stochastic process to random fields via a characteristic of the set A related to the Euler characteristic of differential topology. When X(t) is a homogeneous Gaussian field satisfying certain regularity conditions we obtain an explicit formula for the mean value of this characteristic.

scholarly journals Über Linear Passive Transformationen Stochastischer Prozesse I

1968 ◽  
Vol 23 (10) ◽  
pp. 1430-1438 ◽  
Author(s):  
J. Keller
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Mean Value ◽  
Output Process ◽  
Passive Systems ◽  
Physical Systems ◽  
General Properties ◽  
Input And Output ◽  
The Mean

The theory of linear passive systems, developed by KÖNIG and MEIXNER, is extended to the case where the input is not a well determined function of time but rather a stochastic process. In this case the answer of the system generally will also be a stochastic process. The input and output processes are connected by a linear passive transformation (LPT). Some examples are given of physical systems which may be described by LPT of stochastic processes. General properties of the mean value and the dispersion of the output process are derived.

Excursions above a fixed level by n-dimensional random fields

1976 ◽  
Vol 13 (02) ◽  
pp. 276-289 ◽  
Author(s):  
Robert J. Adler
Keyword(s):  
Stochastic Process ◽  
Random Field ◽  
Random Fields ◽  
Mean Value ◽  
Regularity Conditions ◽  
Gaussian Field ◽  
Differential Topology ◽  
One Dimensional ◽  
Excursion Set ◽  
The Mean

For an n-dimensional random field X(t) we define the excursion set A of X(t) by A = [t ∊ S: X(t) ≧ u] for real u and compact S ⊂ Rn. We obtain a generalisation of the number of upcrossings of a one-dimensional stochastic process to random fields via a characteristic of the set A related to the Euler characteristic of differential topology. When X(t) is a homogeneous Gaussian field satisfying certain regularity conditions we obtain an explicit formula for the mean value of this characteristic.

Sign in / Sign up

Export Citation Format

Share Document