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