scholarly journals High excursions of Bessel process and other processes of Bessel type

2019 ◽  
Vol 487 (3) ◽  
pp. 238-241
Author(s):  
V. I. Piterbarg ◽  
I. V. Rodionov
Keyword(s):  
Single Point ◽  
Bessel Process ◽  
Absolute Maximum ◽  
Time Interval ◽  
Gaussian Vector ◽  
Vector Process ◽  
Distributed Components ◽  
Excursion Probability ◽  
Independent Identically Distributed

A high excursion probability for the modulus of a Gaussian vector process with independent identically distributed components is evaluated. It is assumed that the components have means zero and variances reaching its absolute maximum at a single point of the considered time interval. An important example of such processes is the Bessel process.

Structural analysis of the trajectories of random processes formed in non-linear vibration isolation systems

2021 ◽  
Author(s):  
A.S. Gusev ◽  
L.V. Zinchenko ◽  
S.A. Starodubtseva
Keyword(s):  
Structural Analysis ◽  
Vibration Isolation ◽  
Fundamental Principle ◽  
Statistical Dependence ◽  
Absolute Maximum ◽  
Time Interval ◽  
Apparent Lack ◽  
The Road ◽  
Isolation Systems ◽  
Non Gaussian

When designing technical structures, the safety of their elements is a fundamental principle. This highlights the significance of the proposed solution to the structural analysis of the trajectories of non-Gaussian stationary processes. The solution aims to acquire source data for calculating the stress-strength reliability of structural elements operating under random loads. We analyze an approach that makes it possible to account for the statistical dependence between processes and their derivatives, despite the apparent lack of correlation between them. The considered approach can be utilized in the design of vibration protection of transport vehicles to calculate the probability of a shock absorber breakdown, the probability of loss of the road-wheel contact, etc. The operation reliability of such systems is defined as the probability that the absolute maximum of the process does not exceed the specified standard level during a certain time interval. The article presents the reliability calculation using structural analysis on the example of a one-dimensional stochastic system.

Identification of Forces in Vibrating Plates by Pointwise and Line Observations: Uniqueness and Stability

1995 ◽  
Author(s):  
Masahiro Yamamoto
Keyword(s):  
Finite Time ◽  
Large Time ◽  
Single Point ◽  
Time Interval ◽  
Finite Time Interval ◽  
Line Parallel ◽  
Vibrating Plates ◽  
External Forces ◽  
Spatially Varying

Abstract We consider determination of spatially varying external forces in a rectangle vibrating plate from displacement observed along a line parallel to a side of the plate over a finite time interval. For a suitable choice of the line and a sufficient large time interval, we prove the uniqueness of external forces and estimate them by appropriate norm of displacement. Moreover we discuss determination of external forces from displacement observed at a single point over a time interval.

Signatures of indirect majority systems

2001 ◽  
Vol 38 (2) ◽  
pp. 597-603 ◽  
Author(s):  
Philip J. Boland
Keyword(s):  
Order Statistic ◽  
Coherent System ◽  
Simple Majority ◽  
Distributed Components ◽  
Independent Identically Distributed

If τ is the lifetime of a coherent system, then the signature of the system is the vector of probabilities that the lifetime coincides with the ith order statistic of the component lifetimes. The signature can be useful in comparing different systems. In this treatment we give a characterization of the signature of a system with independent identically distributed components in terms of the number of path sets in the system as well as in terms of the number of what we call ordered cut sets. We consider, in particular, the signatures of indirect majority systems and compare them with the signatures of simple majority systems of the same size. We note that the signature of an indirect majority system of size r × s = n is symmetric around , and use this to show that the expected lifetime of an r × s = n indirect majority system exceeds that of a simple (direct) majority system of size n when the components are exponentially distributed with the same parameter.

Queues with random service output: the case of Poisson arrivals

1974 ◽  
Vol 11 (04) ◽  
pp. 771-784 ◽  
Author(s):  
Jacob Grinstein ◽  
Michael Rubinovitch
Keyword(s):  
Queueing Models ◽  
Time Interval ◽  
Single Server ◽  
Independent Increments ◽  
Virtual Waiting Time ◽  
Two Factors ◽  
Waiting Time Process ◽  
Poisson Arrivals ◽  
Busy Server ◽  
Independent Identically Distributed

A general class of single server queueing models is formulated. They distinguish between two factors that may influence the duration of service times: variability in the service requirements of customers, and variability (over time) in the service output of the server. Accordingly, we assume that the demands for service of successive customers form a sequence of independent, identically distributed random variables and that the amount of service produced by a busy server in a time interval is determined by the increment of a process with stationary independent increments over that interval. The results include the distribution of the busy period and the limiting distribution of the queue length. We also investigate the potential waiting process which is an extension of virtual waiting time process in existing queueing models.

Queues with random service output: the case of Poisson arrivals

1974 ◽  
Vol 11 (4) ◽  
pp. 771-784 ◽  
Author(s):  
Jacob Grinstein ◽  
Michael Rubinovitch
Keyword(s):  
Queueing Models ◽  
Time Interval ◽  
Single Server ◽  
Independent Increments ◽  
Virtual Waiting Time ◽  
Two Factors ◽  
Waiting Time Process ◽  
Poisson Arrivals ◽  
Busy Server ◽  
Independent Identically Distributed

A general class of single server queueing models is formulated. They distinguish between two factors that may influence the duration of service times: variability in the service requirements of customers, and variability (over time) in the service output of the server. Accordingly, we assume that the demands for service of successive customers form a sequence of independent, identically distributed random variables and that the amount of service produced by a busy server in a time interval is determined by the increment of a process with stationary independent increments over that interval. The results include the distribution of the busy period and the limiting distribution of the queue length. We also investigate the potential waiting process which is an extension of virtual waiting time process in existing queueing models.

Density factorizations for brownian motion, meander and the three-dimensional bessel process, and applications

1984 ◽  
Vol 21 (3) ◽  
pp. 500-510 ◽  
Author(s):  
J.-P. Imhof
Keyword(s):  
Brownian Motion ◽  
Three Dimensional ◽  
Fixed Time ◽  
Bessel Process ◽  
Time Interval ◽  
Change Of Measure ◽  
Fixed Time Interval ◽  
Simple Change ◽  
Brownian Meander ◽  
Passage Times

Joint densities concerning in particular the value and time of the maximum over a fixed time interval, or the behavior over intervals determined by some first- and last-passage times, are determined for Brownian motion, the three-dimensional Bessel process and Brownian meander. Simple change of measure formulas permit easy passage from one process to the other. Examples are given.

A Fully Distributed Architecture for Large Scale Workflow Enactment

2003 ◽  
Vol 12 (04) ◽  
pp. 411-440 ◽  
Author(s):  
Roberto Silveira Silva Filho ◽  
Jacques Wainer ◽  
Edmundo R. M. Madeira
Keyword(s):  
Large Scale ◽  
Single Point ◽  
Workflow Management ◽  
Management Systems ◽  
Centralized Control ◽  
Dynamic Allocation ◽  
Workflow Management Systems ◽  
Client Server ◽  
Workflow Execution ◽  
Distributed Components

Standard client-server workflow management systems are usually designed as client-server systems. The central server is responsible for the coordination of the workflow execution and, in some cases, may manage the activities database. This centralized control architecture may represent a single point of failure, which compromises the availability of the system. We propose a fully distributed and configurable architecture for workflow management systems. It is based on the idea that the activities of a case (an instance of the process) migrate from host to host, executing the workflow tasks, following a process plan. This core architecture is improved with the addition of other distributed components so that other requirements for Workflow Management Systems, besides scalability, are also addressed. The components of the architecture were tested in different distributed and centralized configurations. The ability to configure the location of components and the use of dynamic allocation of tasks were effective for the implementation of load balancing policies.

Simulating a non-Gaussian vector process with application in hydrology

2014 ◽  
Vol 41 (6) ◽  
pp. 621-626 ◽  
Author(s):  
A. V. Frolov ◽  
T. Yu. Vyruchalkina ◽  
I. V. Solomonova
Keyword(s):  
Gaussian Vector ◽  
Vector Process ◽  
Non Gaussian

Compactness and single-point blowup of positive solutions on bounded domains

1997 ◽  
Vol 127 (1) ◽  
pp. 47-65 ◽  
Author(s):  
Stathis Filippas ◽  
Frank Merle
Keyword(s):  
Initial Data ◽  
Positive Solutions ◽  
Single Point ◽  
Time Interval ◽  
Bounded Domains ◽  
General Criterion ◽  
Smooth Convex ◽  
Semilinear Heat Equation ◽  
Image Position ◽  
Boundary Solutions

This paper is concerned with the blowup of positive solutions of the semilinear heat equationwith zero boundary conditions. The domainΩis supposed to be smooth, convex and bounded. We first show that, under the assumption that the initial data are uniformly monotone near the boundary, solutions that exist on the time interval (0,Tform a compact family in a suitable topology. We then derive some localisation properties of these solutions. In particular, we discuss a general criterion, independent of the initial data, which in some cases ensures single-point blowup.

Cox limit theorem for large excursions of a norm of a Gaussian vector process

2010 ◽  
Vol 80 (19-20) ◽  
pp. 1479-1485 ◽  
Author(s):  
Biljana Stamatovic ◽  
Sinisa Stamatovic
Keyword(s):  
Limit Theorem ◽  
Gaussian Vector ◽  
Vector Process
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