Table 1.

Results of the set analysis in a Markov chain demographic model.

Output	Expression	Equation
Occupancy time in $\mathcal{B}$
Mean and variance	$\mathbb{E}\left[{\mathit{\tau }}_{\mathcal{B}}\right],\mathrm{Var}\left({\mathit{\tau }}_{\mathcal{B}}\right)$	(20), (24), (25), (26)
Moments	${\mathit{\tau }}_{\mathcal{B}}^k$	(23)–(25)
Distribution		(28)–(29)
Reaching the set $\mathcal{B}$
Probability to reach	${\mathbf{p}}_a$	(39)
Time to reach:	${\mathbf{t}}_{\mathcal{B}}$	(41)
Mean and variance	$\mathbb{E}\left[{\mathbf{t}}_{\mathcal{B}}\right],\mathrm{Var}\left({\mathbf{t}}_{\mathcal{B}}\right)$	(43)–(44)
Moments	${\mathbf{t}}_{\mathcal{B}}^k$	(42)
Distribution		(45)
Returning to the set $\mathcal{B}$
Probability to return	${\mathbf{p}}_r$	(47)
Time to return:	$\mathit{\mu }$	(48)
Mean and variance	$\mathbb{E}\left[\mathit{\mu }\right],\mathrm{Var}\left(\mathit{\mu }\right)$	(53)–(54)
Moments	${\mathit{\mu }}^{\mathbb{K}}$	(97), in the appendix
Distribution		(51)–(52)
Correlation between the occupancy times in two sets
Correlation	$\mathrm{Corr}\left({\mathit{\tau }}_{{\mathcal{B}}_1},{\mathit{\tau }}_{{\mathcal{B}}_2}\right)$	(86)–(36)
Correlation between the occupancy time in $\mathcal{B}$ and the longevity
Correlation	$\mathrm{Corr}\left({\mathit{\tau }}_{\mathcal{B}},\mathit{\eta }\right)$	(38)