Abstract
In this paper, the closed form solution of the non-homogeneous linear first-order difference equation is given. The studied equation is in the form: xn = x0 + bn, where the initial value x0 and b, are random variables.
Highlights
A difference equation or dynamical system describes the evolution of some variable over time
Difference equations relate to differential equations as discrete mathematics relates to continuous mathematics
Anyone who has made a study of differential equations will know that even supposedly elementary examples can be hard to solve
Summary
A difference equation or dynamical system describes the evolution of some variable over time. The value of this variable in period t is denoted by xn. Difference equations relate to differential equations as discrete mathematics relates to continuous mathematics. Difference equation is the most powerful instrument for the treatment of discrete processes. Stochastic difference equations are difference equations with random parameters Such equations arise in various disciplines, for example economics [4], physics, nuclear technology, biology and sociology. We present a new technique based on the direct transformation technique to express analytically the probability density function of the general solution of stochastic linear 1st order difference equations
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