TY - JOUR
ID - 21082
TI - Fractional Probability Measure and Its Properties
JO - Journal of Sciences, Islamic Republic of Iran
JA - JSCIENCES
LA - en
SN - 1016-1104
AU - Mostafaee, H
AD -
Y1 - 2010
PY - 2010
VL - 21
IS - 3
SP - 259
EP - 264
KW - fractional probability measure
KW - Probability density of fractional order ?
KW - fractional probability space
KW - probability measure continuity
DO -
N2 - Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical one. According to the probability principles in classical probability theory and the definition of probability density of fractional order by Guy Jumarie, at first, the fractional probability principles are discussed. Then the fractional probability space is introduced. Consequently, the fractional probability measure , is explained. Moreover, validity of the classical "probability measure continuity" theorem ( ) for the fractional probability measure is verified, which results in "Fatou Lemma" and some theorems in convergence concept.
UR - https://jsciences.ut.ac.ir/article_21082.html
L1 - https://jsciences.ut.ac.ir/article_21082_272ccd830c31497eb4b4d2079397f26b.pdf
ER -