Summary: Multivariate Stieltjes continued fractions
Michael Anshelevich
June 17, 2008
µ = probability measure on R, with all moments finite.
Identify with a functional µ on R[x].
Moments
µ[x], µ[x2], µ[x3], . . . .
Moment generating function
Mµ
(z) = 1 + µ[x]z + µ[x2
]z2
+ µ[x3
]z3
+ . . . .
1
Has a (Stieltjes) continued fractions expansion
Mµ
(z) = 1 + µ[x]z + µ[x2
]z2
+ µ[x3

Source: Anshelevich, Michael - Department of Mathematics, Texas A&M University

Collections: Mathematics