Theory of Chances: Novel Stochastic Chains: Linear Algebraic Approach

Garimella Rama Murthy

doi:10.4172/2168-9679.1000191

Abstract

In this research paper, the author proposes the idea of allowing the chance (like probability) to assume negative and complex values. Novel stochastic chains based on real/complex valued 2p L chances are formally discussed. Also, the theory of 1 L chances is discussed. Chance number theory is briefly discussed.

Highlights

Mathematics as a branch of human endeavour had early beginnings with geometry
Novel Stochastic Chains: Real Valued Chance Case: It should be kept in mind that the “normalized chance” of an event is the sum of squares of chances of the constituent outcomes
In view of the above Theorem, novel stochastic chains characterized by symmetric orthogonal matrix converge to an equilibrium chance vector when V(0) or V(0) F2 = 0 in many practically interesting cases; such a choice of initial chance vector can always be made

Summary

Introduction

Mathematics as a branch of human endeavour had early beginnings with geometry. The efforts of mathematicians led to the fields such as trigonometry, algebra etc. Many branches of mathematics had their beginnings in attempting to solve problems associated with natural and/or artificial phenomena One such branch was classical probability theory. After understanding the concept of fuzzy set, the author reasoned the need for negative membership function in [19] This innovative idea motivated the author to see if a consistent theory can be developed in which the probabilities (called “chances”) are allowed to assume negative values. The author proposed to formalize a consistent theory of stochastic chains based on real, complex valued chances. It is possible to give several real world experiments in which “chances” of outcomes necessarily assume negative values (For instance “summer season” related events SUNNY, CLOUDY, RAINY and the associated temperature values).

Theory of L2p Real Valued Chances

Theory of L2p Complex Valued Chances

Waring Problem

Theory of L1 Chances

Motivation for Alternative Theories of Uncertainity

Conclusions