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Table 1 A summary of mathematical notation for the variables used in definition and calculation of healthy longevity using Markov chains with rewards

From: Matrix methods in health demography: a new approach to the stochastic analysis of healthy longevity and DALYs

Symbol Definition Dimension
P Markov chain transition matrix (ω+a)×(ω+a)
U Survival and age transition matrix ω×ω
M Mortality matrix a×ω
R i Matrix of ith moments of rewards (ω+a)×(ω+a)
ρ i Vector of ith moments of lifetime accumulated reward (ω+a)×1
\(\tilde {\boldsymbol {\rho }}_{i}\) As ρ i , but for living states ω×1
Z 0-1 matrix to select living states ω×(ω+a)
N Fundamental matrix ω×ω
η 1 Vector of ith moments of remaining longevity ω×1
ω Number of age classes scalar
a Number of absorbing (dead) states scalar