Estimating the Probability That a Random Process First Reaches the Boundary of a Region on a Given Time Interval

2018 ◽  
Author(s):  
Sergei L. Semakov ◽  
Ivan S. Semakov
Keyword(s):  
Random Process ◽  
Time Interval

scholarly journals Period-Life of a Branching Process with Migration and Continuous Time

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 868
Author(s):  
Khrystyna Prysyazhnyk ◽  
Iryna Bazylevych ◽  
Ludmila Mitkova ◽  
Iryna Ivanochko
Keyword(s):  
Random Process ◽  
Generating Function ◽  
Continuous Time ◽  
Branching Process ◽  
Probability Generating Function ◽  
Time Interval ◽  
The Moment ◽  
First Time ◽  
Critical Branching Process ◽  
Number Of Particles

The homogeneous branching process with migration and continuous time is considered. We investigated the distribution of the period-life τ, i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time. The probability generating function of the random process, which describes the behavior of the process within the period-life, was obtained. The boundary theorem for the period-life of the subcritical or critical branching process with migration was found.

scholarly journals A Methodology for Multihazards Load Combinations of Earthquake and Heavy Trucks for Bridges

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Dezhang Sun ◽  
Xu Wang ◽  
Baitao Sun
Keyword(s):  
Random Process ◽  
Random Variables ◽  
Load Resistance ◽  
Time Interval ◽  
Modified Model ◽  
Heavy Trucks ◽  
Extreme Load ◽  
Earthquake Load ◽  
Heavy Truck ◽  
Truck Load

Issues of load combinations of earthquakes and heavy trucks are important contents in multihazards bridge design. Currentload resistance factor design(LRFD)specificationsusually treat extreme hazards alone and have no probabilistic basis in extreme load combinations. Earthquake load and heavy truck load are considered as random processes with respective characteristics, and the maximum combined load is not the simple superimposition of their maximum loads. Traditional Ferry Borges-Castaneda model that considers load lasting duration and occurrence probability well describes random process converting to random variables and load combinations, but this model has strict constraint in time interval selection to obtain precise results. Turkstra’s rule considers one load reaching its maximum value in bridge’s service life combined with another load with its instantaneous value (or mean value), which looks more rational, but the results are generally unconservative. Therefore, a modified model is presented here considering both advantages of Ferry Borges-Castaneda's model and Turkstra’s rule. The modified model is based on conditional probability, which can convert random process to random variables relatively easily and consider the nonmaximum factor in load combinations. Earthquake load and heavy truck load combinations are employed to illustrate the model. Finally, the results of a numerical simulation are used to verify the feasibility and rationality of the model.

The distribution of the content of finite dams

1967 ◽  
Vol 4 (1) ◽  
pp. 151-161 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Process ◽  
Time Interval ◽  
Dam Reservoir ◽  
Continuous Release ◽  
Excess Water ◽  
Constant Unit

We shall consider the following model of finite dams: In the time interval (0, ∞) water is flowing into a dam (reservoir) in accordance with a random process. Denote by χ(u) the total quantity of water flowing into the dam in the time interval (0, u). The capacity of the dam is a finite positive number m. If the dam becomes full, the excess water overflows. If the dam is not empty, there is a continuous release at a constant unit rate. Denote by η(t) the content of the dam at time t.

scholarly journals Application of probability and statistics methods in arrangement of railway transportation

2018 ◽  
Vol 216 ◽  
pp. 02004 ◽  
Author(s):  
Grigory Gefan
Keyword(s):  
Random Process ◽  
Time Interval ◽  
Training Methods ◽  
Railway Transportation ◽  
Mathematical Methods ◽  
Railway Stations ◽  
Exponential Law ◽  
Probability And Statistics ◽  
Independence Of Events ◽  
Active Training

Complex economic and mathematical methods are becoming more widespread in training of specialists in the field of railroad communication arrangement. The purpose of this study is to develop an effective methodology for mathematical training of railway transportation specialists on the basis of active training methods. The article deals with application of probabilistic and statistical methods to problems in design of railway transportation, for example, fluctuations in loading of railway stations and distribution of the time interval between arrival of trains. Using the example of the flow of arriving trains, the technology of testing the hypothesis that the time between arrival of trains is distributed according to the exponential law and the hypothesis of independence of events in the flow is displayed in detail. When confirming each of these hypotheses, it must be concluded that the flow of trains arriving at the station is according to the simplest (Poisson’s) model. This conclusion allows using the apparatus of Markov chains to describe a random process.

The distribution of the content of finite dams

1967 ◽  
Vol 4 (01) ◽  
pp. 151-161 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Process ◽  
Time Interval ◽  
Dam Reservoir ◽  
Continuous Release ◽  
Excess Water ◽  
Constant Unit

We shall consider the following model of finite dams: In the time interval (0, ∞) water is flowing into a dam (reservoir) in accordance with a random process. Denote by χ(u) the total quantity of water flowing into the dam in the time interval (0, u). The capacity of the dam is a finite positive number m. If the dam becomes full, the excess water overflows. If the dam is not empty, there is a continuous release at a constant unit rate. Denote by η(t) the content of the dam at time t.

Focusing of Visuospatial Attention

2001 ◽  
Vol 15 (4) ◽  
pp. 256-274 ◽  
Author(s):  
Caterina Pesce ◽  
Rainer Bösel
Keyword(s):  
Reaction Times ◽  
Visual Space ◽  
Spatial Relation ◽  
Stimulus Onset ◽  
Visuospatial Attention ◽  
Task Demands ◽  
Time Interval ◽  
Behavioral Studies ◽  
Task Conditions ◽  
Simple Rt

Abstract In the present study we explored the focusing of visuospatial attention in subjects practicing and not practicing activities with high attentional demands. Similar to the studies of Castiello and Umiltà (e. g., 1990) , our experimental procedure was a variation of Posner's (1980) basic paradigm for exploring covert orienting of visuospatial attention. In a simple RT-task, a peripheral cue of varying size was presented unilaterally or bilaterally from a central fixation point and followed by a target at different stimulus-onset-asynchronies (SOAs). The target could occur validly inside the cue or invalidly outside the cue with varying spatial relation to its boundary. Event-related brain potentials (ERPs) and reaction times (RTs) were recorded to target stimuli under the different task conditions. RT and ERP findings showed converging aspects as well as dissociations. Electrophysiological results revealed an amplitude modulation of the ERPs in the early and late Nd time interval at both anterior and posterior scalp sites, which seems to be related to the effects of peripheral informative cues as well as to the attentional expertise. Results were: (1) shorter latency effects confirm the positive-going amplitude enhancement elicited by unilateral peripheral cues and strengthen the criticism against the neutrality of spatially nonpredictive peripheral cueing of all possible target locations which is often presumed in behavioral studies. (2) Longer latency effects show that subjects with attentional expertise modulate the distribution of the attentional resources in the visual space differently than nonexperienced subjects. Skilled practice may lead to minimizing attentional costs by automatizing the use of a span of attention that is adapted to the most frequent task demands and endogenously increases the allocation of resources to cope with less usual attending conditions.

Attention Deficit and Disruptive Behavior Disorder Symptoms

2001 ◽  
Vol 17 (1) ◽  
pp. 25-35 ◽  
Author(s):  
G. Leonard Burns ◽  
James A. Walsh ◽  
David R. Patterson ◽  
Carol S. Holte ◽  
Rita Sommers-Flanagan ◽  
...  
Keyword(s):  
Attention Deficit ◽  
Rating Scales ◽  
Behavior Disorder ◽  
Disruptive Behavior Disorder ◽  
Subjective Rating ◽  
Time Interval ◽  
Assessment Procedure ◽  
Frequency Count ◽  
Hyperactivity Disorder ◽  
Oppositional Defiant

Summary: Rating scales are commonly used to measure the symptoms of attention deficit/hyperactivity disorder (ADHD), oppositional defiant disorder (ODD), and conduct disorder (CD). While these scales have positive psychometric properties, the scales share a potential weakness - the use of vague or subjective rating procedures to measure symptom occurrence (e. g., never, occasionally, often, and very often). Rating procedures based on frequency counts for a specific time interval (e. g., never, once, twice, once per month, once per week, once per day, more than once per day) are less subjective and provide a conceptually better assessment procedure for these symptoms. Such a frequency count procedure was used to obtain parent ratings on the ADHD, ODD, and CD symptoms in a normative (nonclinical) sample of 3,500 children and adolescents. Although the current study does not provide a direct comparison of the two types of rating procedures, the results suggest that the frequency count procedure provides a potentially more useful way to measure these symptoms. The implications of the results are noted for the construction of rating scales to measure the ADHD, ODD, and CD symptoms.

Sign in / Sign up

Export Citation Format

Share Document