On single-lane roads

1989 ◽  
Vol 21 (1) ◽  
pp. 142-158
Author(s):  
A. J. Koning
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Processes ◽  
Large Distance ◽  
Random Variable ◽  
Exponential Random Variable ◽  
Speed Distribution

A road which narrows at a bottleneck from an ∞-lane road to a one-lane road is studied with the aid of two stochastic processes. Special attention is given to headways and gaps. At the bottleneck an equilibrium headway can be viewed as the maximum of a shifted exponential random variable and a minimum headway. After the bottleneck the situation becomes far more complicated. However, limiting results are obtained for headways and gaps at a large distance from the bottleneck. The asymptotic behavior of headways and gaps is largely determined by the behavior of the desired speed distribution at the lower extreme of its support.

On single-lane roads

1989 ◽  
Vol 21 (01) ◽  
pp. 142-158
Author(s):  
A. J. Koning
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Processes ◽  
Large Distance ◽  
Random Variable ◽  
Exponential Random Variable ◽  
Speed Distribution

A road which narrows at a bottleneck from an ∞-lane road to a one-lane road is studied with the aid of two stochastic processes. Special attention is given to headways and gaps. At the bottleneck an equilibrium headway can be viewed as the maximum of a shifted exponential random variable and a minimum headway. After the bottleneck the situation becomes far more complicated. However, limiting results are obtained for headways and gaps at a large distance from the bottleneck. The asymptotic behavior of headways and gaps is largely determined by the behavior of the desired speed distribution at the lower extreme of its support.

THE ASYMPTOTIC BEHAVIOR OF SEMI-INVARIANTS FOR LINEAR STOCHASTIC SYSTEMS

2002 ◽  
Vol 02 (02) ◽  
pp. 281-294
Author(s):  
G. N. MILSTEIN
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Exponent ◽  
Linear System ◽  
Characteristic Function ◽  
Stochastic Systems ◽  
Random Variable ◽  
Characteristic Functions ◽  
Linear Stochastic Systems ◽  
Moment Lyapunov Exponent ◽  
The Moment

The asymptotic behavior of semi-invariants of the random variable ln |X(t,x)|, where X(t,x) is a solution of a linear system of stochastic differential equations, is connected with the moment Lyapunov exponent g(p). Namely, it is obtained that the nth semi-invariant is asymptotically proportional to the time t with the coefficient of proportionality g(n)(0). The proof is based on the concept of analytic characteristic functions. It is also shown that the asymptotic behavior of the analytic characteristic function of ln |X(t,x)| in a neighborhood of the origin of the complex plane is controlled by the extension g(iz) of g(p).

A generalized spatial-temporal model of rainfall based on a clustered point process

1995 ◽  
Vol 450 (1938) ◽  
pp. 163-175 ◽  
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Random Variable ◽  
Cell Types ◽  
Exponential Random Variable ◽  
Two Dimensional ◽  
Arrival Times ◽  
Hourly Rainfall ◽  
Temporal Model ◽  
Different Cell Types

The objective in this paper is to present and fit a relatively simple stochastic spatial-temporal model of rainfall in which the arrival times of rain cells occur in a clustered point process. In the x - y plane, rain cells are represented as discs; each disc having a random radius; the locations of the disc centres being given by a two-dimensional Poisson process. The intensity of each cell is a random variable that remains constant over the area of the disc and throughout the lifetime of the cell, the lifetime being an exponential random variable. The cells are randomly classified from 1 to n with different parameters for the different cell types, so that the random variables of an arbitrary cell, e. g. radius and intensity, are correlated. Multi-site second-order properties are derived and used to fit the model to hourly rainfall data taken from six sites in the Thames basin, UK.

scholarly journals Hermite-Hadamard, Jensen, and Fractional Integral Inequalities for Generalized P -Convex Stochastic Processes

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Fangfang Ma ◽  
Waqas Nazeer ◽  
Mamoona Ghafoor
Keyword(s):  
Probability Theory ◽  
Convex Function ◽  
Stochastic Processes ◽  
Fractional Integral ◽  
Probabilistic Models ◽  
Random Variable ◽  
Expected Value ◽  
Integral Inequalities ◽  
Stochastic Convexity ◽  
Convex Stochastic Processes

The stochastic process is one of the important branches of probability theory which deals with probabilistic models that evolve over time. It starts with probability postulates and includes a captivating arrangement of conclusions from those postulates. In probability theory, a convex function applied on the expected value of a random variable is always bounded above by the expected value of the convex function of that random variable. The purpose of this note is to introduce the class of generalized p -convex stochastic processes. Some well-known results of generalized p -convex functions such as Hermite-Hadamard, Jensen, and fractional integral inequalities are extended for generalized p -stochastic convexity.

scholarly journals Multi-type branching processes with time-dependent branching rates

2018 ◽  
Vol 55 (3) ◽  
pp. 701-727 ◽  
Author(s):  
D. Dolgopyat ◽  
P. Hebbar ◽  
L. Koralov ◽  
M. Perlman
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Random Variable ◽  
Time Dependent ◽  
Exponential Random Variable ◽  
Number Of Particles

Abstract Under mild nondegeneracy assumptions on branching rates in each generation, we provide a criterion for almost sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total number of particles (conditioned on survival and divided by the expectation of the resulting random variable) to approach an exponential random variable as time goes to ∞.

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