Introduction to Neutrosophic Stochastic Processes

Abstract

In this article, the definition of literal neutrosophic stochastic processes is presented for the first time in the form 𝒩𝑡 = 𝜉𝑡 + 𝜂𝑡𝐼 ;𝐼 2 = 𝐼 where both {𝜉(𝑡),𝑡 ∈ 𝑇} and {𝜂(𝑡),𝑡 ∈ 𝑇} are classical real valued stochastic processes. Characteristics of the literal neutrosophic stochastic process are defined and its formulas are driven including neutrosophic ensemble mean, neutrosophic covariance function and neutrosophic autocorrelation function. Concept of literal neutrosophic stationary stochastic processes is well defined and many theorems are presented and proved using classical neutrosophic operations then using the one-dimensional AH-Isometry. Some solved examples are presented and solved successfully. We have proved that studying the literal neutrosophic stochastic process {𝒩(𝑡),𝑡 ∈ 𝑇} is equivalent to studying two classical stochastic processes which are {𝜉(𝑡),𝑡 ∈ 𝑇} and {𝜉 𝑡 + 𝜂𝑡 ,𝑡 ∈ 𝑇}.

Keywords

• ah-isometry
• neutrosophic field of reals
• neutrosophic random variables
• stationary stochastic processes
• characteristics of stochastic processes
• ensemble mean
• covariance function
• autocorrelation function