Introduction to Neutrosophic Stochastic Processes

Mohamed Bisher Zeina; Yasin Karmouta

Authors

Mohamed Bisher Zeina Faculty of Science, Dept. of Mathematical Statistics, University of Aleppo, Aleppo, Syria;
Yasin Karmouta Faculty of Science, Dept. of Mathematical Statistics, University of Aleppo, Aleppo, Syria;

Keywords:

AH-Isometry; Neutrosophic Field of Reals; Neutrosophic Random Variables; Stationary Stochastic Processes; Characteristics of Stochastic Processes; Ensemble Mean; Covariance Function; Autocorrelation Function.

Abstract

: In this article, the definition of literal neutrosophic stochastic processes is
presented for the first time in the form ð’©ð‘¡ = ðœ‰ð‘¡ + ðœ‚ð‘¡ð¼ ;ð¼
2 = ð¼ where both {ðœ‰(ð‘¡),ð‘¡ âˆˆ ð‘‡} and
{ðœ‚(ð‘¡),ð‘¡ âˆˆ ð‘‡} 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 {ð’©(ð‘¡),ð‘¡ âˆˆ ð‘‡} is equivalent to studying two classical stochastic processes
which are {ðœ‰(ð‘¡),ð‘¡ âˆˆ ð‘‡} and {ðœ‰
ð‘¡ + ðœ‚ð‘¡
,ð‘¡ âˆˆ ð‘‡}.