Estimating the Mean of an Increasing Stochastic Process at a Censored Stopping Time

2000 ◽  
Vol 95 (452) ◽  
pp. 1192-1208 ◽  
Author(s):  
Robert L. Strawderman
Keyword(s):  
Stochastic Process ◽  
Stopping Time ◽  
The Mean

About the # Function

1976 ◽  
Vol 19 (4) ◽  
pp. 455-460
Author(s):  
G. T. Klincsek
Keyword(s):  
Stochastic Process ◽  
Stopping Time ◽  
Decreasing Rearrangement ◽  
Image Position

AbstractThe use of decreasing rearrangement formulas, and particularly that of the weak N inequality, is illustrated by deriving from Eτ |f-f(τ -)|≤Eτu (where ft is some stochastic process and τ arbitrary stopping time) the estimate ||f||≤Const||u|| in the class of structureless norms with finite dual Hardy bound.The basic estimate is

On Sequential Procedures for the Point Estimation of the Mean Vector

1988 ◽  
Vol 37 (1-2) ◽  
pp. 47-54 ◽  
Author(s):  
R. Karan Singh ◽  
Ajit Chaturvedi
Keyword(s):  
Normal Population ◽  
Stopping Time ◽  
Point Estimation ◽  
Multivariate Normal ◽  
Minimum Risk ◽  
Sequential Procedures ◽  
Multivariate Normal Population ◽  
Bounded Risk ◽  
The Mean ◽  
Mean Vector

Sequential procedures are proposed for (a) the minimum risk point estimation and (b) the bounded risk point estimation of the mean vector of a multivariate normal population . Second-order approximations are derived. For the problem (b), a lower bound for the number of additional observations (after stopping time) is obtained which ensures “ exact” boundedness of the risk associated witb the sequential procedure.

Research on Stock Analysis Based on Stochastic Process

2012 ◽  
Vol 433-440 ◽  
pp. 5967-5974
Author(s):  
Pei Ze Li
Keyword(s):  
Stochastic Process ◽  
Stock Prices ◽  
Stock Price ◽  
Statistical Physics ◽  
Stopping Time ◽  
Mathematical Finance ◽  
Market Condition ◽  
Price Process ◽  
Physics Model ◽  
Statistical Physics Model

In stock market, the stock prices directly reflects market condition, therefore, the research on stock price process is one of the research contents of mathematical finance. In this paper by using the election model of statistical physics model to study the stock price fluctuation . This paper first applying stochastic process theory to establish election model, then the election model and stopping time theory are applied to establish stock profit process, we get the stock price process.

An Upper Bound on the Failure Probability for Linear Structures

1973 ◽  
Vol 40 (1) ◽  
pp. 181-185 ◽  
Author(s):  
L. H. Koopmans ◽  
C. Qualls ◽  
J. T. P. Yao
Keyword(s):  
Stochastic Process ◽  
Failure Probability ◽  
Upper Bound ◽  
Impulse Response Function ◽  
Linear Structures ◽  
Stochastic Response ◽  
Gaussian Stochastic Process ◽  
Exponential Bound ◽  
Mean And Variance ◽  
The Mean

This paper establishes a new upper bound on the failure probability of linear structures excited by an earthquake. From Drenick’s inequality max|y(t)| ≤ MN, where N2 = ∫h2, M2, = ∫x2, x(t) is a nonstationary Gaussian stochastic process representing the excitation of the earthquake, and y(t) is the stochastic response of the structure with impulse response function h(τ), we obtain an exponential bound computable in terms of the mean and variance of the energy M2. A numerical example is given.

scholarly journals A remark on optimal variance stopping problems

2015 ◽  
Vol 52 (4) ◽  
pp. 1187-1194 ◽  
Author(s):  
Bruno Buonaguidi
Keyword(s):  
Stochastic Process ◽  
Diffusion Process ◽  
Interest Rates ◽  
Solution Method ◽  
Stopping Time ◽  
Initial Problem

In an optimal variance stopping problem the goal is to determine the stopping time at which the variance of a sequentially observed stochastic process is maximized. A solution method for such a problem has been recently provided by Pedersen (2011). Using the methodology developed by Pedersen and Peskir (2012), our aim is to show that the solution to the initial problem can be equivalently obtained by constraining the variance stopping problem to the expected size of the stopped process and then by maximizing the solution to the latter problem over all the admissible constraints. An application to a diffusion process used for modeling the dynamics of interest rates illustrates the proposed technique.

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.

STATISTICAL INFERENCE FOR K INDEPENDENT, HOMOGENEOUS ARITHMETIC PROCESSES

2000 ◽  
Vol 07 (03) ◽  
pp. 223-236 ◽  
Author(s):  
FRANCIS KIT-NAM LEUNG
Keyword(s):  
Stochastic Process ◽  
Linear Regression ◽  
Renewal Process ◽  
Random Variable ◽  
Simple Linear Regression ◽  
Variable Formula ◽  
Mean And Variance ◽  
The Mean ◽  
Time Continuum ◽  
Area Of Application

For k=1,…, K, a stochastic process {An,k, n =1, 2,…} is an arithmetic process (AP) if there exists some real number, d, so that {An,k +(n-1)d, n =1, 2,…} is a renewal process (RP). AP is a stochastically monotonic process and can be used to model a point process, i.e., point events occurring in a haphazard way in time (or space), especially with a trend. For example, the events may be failures arising from a deteriorating machine; and such a series of failures is distributed haphazardly along a time continuum. In this paper, we discuss estimation procedures for K independent, homogeneous APs. Two statistics are suggested for testing whether K given processes come from a common AP. If this is so, we can estimate the parameters d, [Formula: see text] and [Formula: see text] of the AP based on the techniques of simple linear regression, where [Formula: see text] and [Formula: see text] are the mean and variance of the first average random variable [Formula: see text], respectively. In this paper, the procedures are, for the most part, discussed in reliability terminology. Of course, the methods are valid in any area of application, in which case they should be interpreted accordingly.

scholarly journals Approximating the Solution Stochastic Process of the Random Cauchy One-Dimensional Heat Model

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
A. Navarro-Quiles ◽  
J.-V. Romero ◽  
M.-D. Roselló ◽  
M. A. Sohaly
Keyword(s):  
Stochastic Process ◽  
Standard Deviation ◽  
Finite Difference ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Sufficient Conditions ◽  
Numerical Approximations ◽  
One Dimensional ◽  
The Mean ◽  
Theoretical Results

This paper deals with the numerical solution of the random Cauchy one-dimensional heat model. We propose a random finite difference numerical scheme to construct numerical approximations to the solution stochastic process. We establish sufficient conditions in order to guarantee the consistency and stability of the proposed random numerical scheme. The theoretical results are illustrated by means of an example where reliable approximations of the mean and standard deviation to the solution stochastic process are given.

On the estimation of the mean of a stochastic process

Automatica ◽  
1975 ◽  
Vol 11 (5) ◽  
pp. 525-527
Author(s):  
Janusz Łaski ◽  
Aleksander Bzowy
Keyword(s):  
Stochastic Process ◽  
The Mean
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