Estimation of longrun variance of continuous time stochastic process using discrete sample

2019 ◽  
Vol 210 (2) ◽  
pp. 236-267 ◽  
Author(s):  
Ye Lu ◽  
Joon Y. Park
Keyword(s):  
Stochastic Process ◽  
Continuous Time ◽  
Discrete Sample ◽  
Continuous Time Stochastic Process

On some properties of the scan statistic on the circle and the line

1977 ◽  
Vol 14 (2) ◽  
pp. 272-283 ◽  
Author(s):  
Noel Cressie
Keyword(s):  
Stochastic Process ◽  
Continuous Time ◽  
Null Hypothesis ◽  
Nuisance Parameter ◽  
Test Statistic ◽  
Scan Statistic ◽  
Asymptotic Power ◽  
Power Comparisons ◽  
Continuous Time Stochastic Process ◽  
Parameter Distributions

The scan statistic is defined as the supremum of a particular continuous-time stochastic process, and is used as a test statistic for testing uniformity against a simple clustering type of alternative. Its distribution under the null hypothesis is investigated and weak convergence of the stochastic process to the appropriate Gaussian process is proved. An interesting link is forged between the circular scan statistic and Kuiper's statistic, which rids us of the trouble of estimating a nuisance parameter. Distributions under the alternative are then derived, and asymptotic power comparisons are made.

scholarly journals Long-Time Behaviour in a Model of Microtubule Growth

2010 ◽  
Vol 42 (1) ◽  
pp. 268-291
Author(s):  
O. Hryniv ◽  
M. Menshikov
Keyword(s):  
Stochastic Process ◽  
Continuous Time ◽  
Complete Characterization ◽  
Time Behaviour ◽  
Local Growth ◽  
Long Time Behaviour ◽  
Long Time ◽  
Microtubule Growth ◽  
Continuous Time Stochastic Process

We study a continuous-time stochastic process on strings made of two types of particle, whose dynamics mimic the behaviour of microtubules in a living cell; namely, the strings evolve via a competition between (local) growth/shrinking as well as (global) hydrolysis processes. We give a complete characterization of the phase diagram of the model, and derive several criteria of the transient and recurrent regimes for the underlying stochastic process.

scholarly journals Modeling the Energy Harvested by an RF Energy Harvesting System Using Gamma Processes

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Inma T. Castro ◽  
Luis Landesa ◽  
Alberto Serna
Keyword(s):  
Stochastic Process ◽  
Energy Harvesting ◽  
Performance Measures ◽  
Continuous Time ◽  
Gamma Process ◽  
Stochastic Characterization ◽  
Energy Harvesting System ◽  
Gamma Processes ◽  
Continuous Time Stochastic Process

In an Energy Harvesting system (EHS) the gamma process is used to model the electromagnetic energy received from radiofrequency (RF) radiation. The stochastic characterization of the harvested energy as a continuous-time stochastic process, namely, gamma process, is obtained from the Nakagami-m fading model, which describes the signal reception in a large amount of types of radiofrequency channels. Using the gamma process, some performance measures of the EHS system are obtained. Also, a transmission policy subject to different fading conditions is considered.

On some properties of the scan statistic on the circle and the line

1977 ◽  
Vol 14 (02) ◽  
pp. 272-283 ◽  
Author(s):  
Noel Cressie
Keyword(s):  
Stochastic Process ◽  
Continuous Time ◽  
Null Hypothesis ◽  
Nuisance Parameter ◽  
Test Statistic ◽  
Scan Statistic ◽  
Asymptotic Power ◽  
Power Comparisons ◽  
Continuous Time Stochastic Process ◽  
Parameter Distributions

The scan statistic is defined as the supremum of a particular continuous-time stochastic process, and is used as a test statistic for testing uniformity against a simple clustering type of alternative. Its distribution under the null hypothesis is investigated and weak convergence of the stochastic process to the appropriate Gaussian process is proved. An interesting link is forged between the circular scan statistic and Kuiper's statistic, which rids us of the trouble of estimating a nuisance parameter. Distributions under the alternative are then derived, and asymptotic power comparisons are made.

Stochastic Process Models of Preference Change

2019 ◽  
pp. 664-682
Author(s):  
Michel Regenwetter ◽  
Yung-Fong Hsu
Keyword(s):  
Stochastic Process ◽  
Decision Theory ◽  
Continuous Time ◽  
Process Models ◽  
Mathematical Psychology ◽  
Preference Change ◽  
Overt Behavior ◽  
Hypothetical Construct ◽  
Feeling Thermometer ◽  
Continuous Time Stochastic Process

This chapter gives an informal summary of a research program aiming to develop and test stochastic process models of preference change. What does it take to develop a formally precise and descriptively valid model of persuasion? Any such model should specify formally concise definitions of hypothetical constructs such as preferences or attitudes. The chapter reviews weak order and semiorder models of preferences that are grounded in decision theory. Such a model should also spell out how hypothetical constructs relate to observable behavior, such as feeling thermometer ratings. The chapter reviews response processes that, in some cases, accommodate within and across respondent heterogeneity in overt behavior. The model should furthermore specify formally what it means to change one’s preference over time and how that change relates to the persuasive environment. The chapter treats preference change as a continuous time stochastic process on a graph of preference states. The most innovative feature of the approach is to model the (perceived) persuasive environment itself also as a hypothetical construct that is not directly/objectively observable by the researcher. Last but not least, the chapter discusses how to accommodate partisan differences, how to incorporate respondents with immutable preferences, and the possibility that respondents may tune in and out of a persuasive campaign. The emphasis of the chapter lies in explaining key conceptual ideas grounded in decision theory and mathematical psychology.

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