2016/11/12 by Romesh Kumar, Kumar, Romesh, Kailash Chand Sharma +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1611.06850
openalex publication_date 2016/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce the concept of hyperbolic valued random variables, their expectation and moments. We develop the hyperbolic analogue of Binomial and Poisson distributions. We study some of the properties of expectation on the basis of decomposition of a hyperbolic number into idempotent components. Finally we define conditional expectation of hyperbolic valued random variable and study some of its basic properties. Our random variable can take values which are zero divisors and this is the important part of this study.