Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation

Econometrica ◽  
1977 ◽  
Vol 45 (2) ◽  
pp. 463 ◽  
Author(s):  
P. C. B. Phillips
Keyword(s):  
Difference Equation ◽  
Finite Sample ◽  
Stochastic Difference Equation ◽  
First Order

Linear Stochastic Difference Equations

2013 ◽  
Author(s):  
Lars Peter Hansen ◽  
Thomas J. Sargent
Keyword(s):  
Time Series ◽  
Difference Equation ◽  
Difference Equations ◽  
Martingale Difference ◽  
Stochastic Difference Equation ◽  
Stochastic Difference Equations ◽  
Order Linear ◽  
Economic Agents ◽  
First Order ◽  
Competitive Equilibria

This chapter describes the vector first-order linear stochastic difference equation. It is first used to represent information flowing to economic agents, then again to represent competitive equilibria. The vector first-order linear stochastic difference equation is associated with a tidy theory of prediction and a host of procedures for econometric application. Ease of analysis has prompted the adoption of economic specifications that cause competitive equilibria to have representations as vector first-order linear stochastic difference equations. Because it expresses next period's vector of state variables as a linear function of this period's state vector and a vector of random disturbances, a vector first-order vector stochastic difference equation is recursive. Disturbances that form a “martingale difference sequence” are basic building blocks used to construct time series. Martingale difference sequences are easy to forecast, a fact that delivers convenient recursive formulas for optimal predictions of time series.

scholarly journals Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
G. M. Moremedi ◽  
I. P. Stavroulakis
Keyword(s):  
Positive Integer ◽  
Difference Equation ◽  
Difference Equations ◽  
Delay Difference Equation ◽  
Real Numbers ◽  
First Order ◽  
All Solutions ◽  
Delay Difference ◽  
Constant Argument

Consider the first-order delay difference equation with a constant argument Δxn+pnxn-k=0,  n=0,1,2,…, and the delay difference equation with a variable argument Δxn+pnxτn=0,  n=0,1,2,…, where p(n) is a sequence of nonnegative real numbers, k is a positive integer, Δx(n)=x(n+1)-x(n), and τ(n) is a sequence of integers such that τ(n)≤n-1 for all n≥0 and limn→∞τ(n)=∞. A survey on the oscillation of all solutions to these equations is presented. Examples illustrating the results are given.

AN OSCILLATION CRITERION FOR FIRST ORDER DIFFERENCE EQUATION

2020 ◽  
Vol 33 (01) ◽  
Author(s):  
Thaniyarasu Kumar ◽  
◽  
Govindasamy Ayyappan ◽  
Keyword(s):  
Difference Equation ◽  
Oscillation Criterion ◽  
Order Difference ◽  
First Order ◽  
Order Difference Equation

scholarly journals Oscillation of First-order Neutral Difference Equation

2009 ◽  
Vol 3 (8) ◽  
Author(s):  
Xiaohui Gong ◽  
Xiaozhu Zhong ◽  
Jianqiang Jia ◽  
Rui Ouyang ◽  
Hongqiang Han
Keyword(s):  
Difference Equation ◽  
Neutral Difference Equation ◽  
First Order
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