TY - JOUR
T1 - Kolmogorov’s Axioms for Probabilities with Values in Hyperbolic Numbers
AU - Alpay, Daniel
AU - Luna-Elizarrarás, M. Elena
AU - Shapiro, Michael
N1 - Publisher Copyright:
© 2016, Springer International Publishing.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - We introduce the notion of a probabilistic measure which takes values in hyperbolic numbers and which satisfies the system of axioms generalizing directly Kolmogorov’s system of axioms. We show that this new measure verifies the usual properties of a probability; in particular, we treat the conditional hyperbolic probability and we prove the hyperbolic analogues of the multiplication theorem, of the law of total probability and of Bayes’ theorem. Our probability may take values which are zero-divisors and we discuss carefully this peculiarity.
AB - We introduce the notion of a probabilistic measure which takes values in hyperbolic numbers and which satisfies the system of axioms generalizing directly Kolmogorov’s system of axioms. We show that this new measure verifies the usual properties of a probability; in particular, we treat the conditional hyperbolic probability and we prove the hyperbolic analogues of the multiplication theorem, of the law of total probability and of Bayes’ theorem. Our probability may take values which are zero-divisors and we discuss carefully this peculiarity.
UR - http://www.scopus.com/inward/record.url?scp=84978818243&partnerID=8YFLogxK
U2 - 10.1007/s00006-016-0706-6
DO - 10.1007/s00006-016-0706-6
M3 - Artículo
SN - 0188-7009
VL - 27
SP - 913
EP - 929
JO - Advances in Applied Clifford Algebras
JF - Advances in Applied Clifford Algebras
IS - 2
ER -