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Renewal Equation

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Journal Article
Demography (1974) 11 (4): 563–585.
Published: 01 November 1974
... well with the theory, as the “Easterlin Hypothesis” suggests; but the period model fits better than the cohort model. 26 1 2011 © Population Association of America 1974 1974 Generational Cycle Cohort Size Period Model Cohort Model Renewal Equation References Anderson T...
Journal Article
Demography (1978) 15 (1): 135–137.
Published: 01 February 1978
... any net maternity function to another and, thus, includes all previous models. 27 1 2011 © Population Association of America 1978 1978 Fertility Decline Renewal Equation Time Dependent Transition Asymptotic Birth Rate Ternity Function References Cerone , P...
Journal Article
Demography (1975) 12 (3): 447–454.
Published: 01 August 1975
..." of popu- lation growth. THE SHORT-TIME SOLUTION The instantaneous rate of female births at time t, B (t), for a, population which is closed to migration can be found from Lotka's (1939) renewal equation B(t) = fa> po(x - t) \lex)flex - t) I ·m(x, t) dx + LB(t - x) l(x) m(x, t) dx, t > 0, (1) where Po(x...
Journal Article
Demography (1989) 26 (1): 99–115.
Published: 01 February 1989
... Mathematics , 40 , 266 – 278 . 10.1137/0140023 Swick , K. ( 1985 ). Some reducible models of age-dependent dynamics . SJAM Journal of Applied Mathematics , 45 , 256 – 267 . 10.1137/0145013 Tuljapurkar , S. ( 1987 ). Cycles in nonlinear age-structured models I: Renewal equations...
Journal Article
Demography (1978) 15 (1): 131–134.
Published: 01 February 1978
... 2011 © Population Association of America 1978 1978 Gradual Change Total Birth Rate Renewal Equation Discontinuous Model Desire Birth Rate References Cerone , P. , & Keane , A. ( 1978 ). The Stable Births Resulting From a Time Dependent Change Between Two Net...
Journal Article
Demography (1972) 9 (2): 309–320.
Published: 01 May 1972
... as the renewal equation (Key- fitz, 1968): 11""bet) = 2" . 0 nmf(a)b(t - a) da with nmf(a) = net maternity function = age specificbirthrate Xprob- ability of survival .. i nmf(a) = L II hi = nmfl + nmf2 '-1 0 + +nmf.. nmfl = ho**hl = contribution of first child to nmf(a) nmf2 = hh1**hz = contribution of second...
Journal Article
Demography (1967) 4 (2): 680–687.
Published: 01 June 1967
... ). On the Integral Equation of Renewal Theory . Annals of Mathematical Statistics , 12 , 243 – 243 10.1214/aoms/1177731708 . 5 Lotka , Alfred ( 1934 ). Theorie Analytique des Associations Bilogiques (pp. 65 – 65 ). Paris : Hermann et Cie . 6 Lopez , Alvaro ( 1961 ). Problems...
Journal Article
Demography (2024) 61 (2): 419–438.
Published: 01 April 2024
... population with constant mortality undergoing a steady decline in fertility rates. Specifically, the net maternity function in Coale's renewal equation has the form φ( a,t ) = φ 0 ( a ) e kt with age a , time t , and constant k < 0, so the period net reproduction rate (NRR) declines exponentially...
FIGURES
Journal Article
Demography (1974) 11 (3): 473–481.
Published: 01 August 1974
... 473 A recent paper by LeBras (1971) introduces a model of the process of population renewal that is the continuous analog of the discrete matrix model of multiregional population growth (Rogers, 1966). In it LeBras develops the following multiregional generalization of the Lotka integral equation: IB...
Journal Article
Demography (2002) 39 (1): 65–73.
Published: 01 February 2002
... in renewal theory. For 0 m 1, all cohorts born after time t = 0 are subject to the stationary net maternity function 2(a). Accordingly, the renewal equation following the transition will take the form B t a B t a da g t t ( ) ( ) ( ) ( + 20 0 t > 0 (4) where B(t) is the stream of births at time t...
Journal Article
Demography (1983) 20 (1): 79–86.
Published: 01 February 1983
... root of (4» is dependent only on the net maternity function, and Q through (6) is a function of both the initial conditions and of r. If the net maternity function cI>(x, t) is allowed to vary with time t, then from (1) the generalized renewal equation for B(t) is given by B(t) = F(t) + 1: B(t - x)cI...
Journal Article
Demography (1990) 27 (4): 639–652.
Published: 01 November 1990
... . Tuliapurkar , S. ( 1987 ). Cycles in Non-linear Age-Structured Models. I: Renewal Equations . Theoretical Population Biology , 32 , 26 – 41 . 10.1016/0040-5809(87)90037-2 Vaupel , J. W. ( 1986 ). How Change in Age-Specific Mortality Affects Life Expectancy . Population Studies , 40...
Journal Article
Demography (1976) 13 (4): 571–575.
Published: 01 November 1976
...Linton C. Freeman; Morris H. Sunshine Abstract Data from the urban renewal experience in Syracuse, New York are used to examine the impact of race on patterns of intra-urban migration. The results show that, overall, the migration patterns exhibited an exponential decay in frequency with increasing...
Journal Article
Demography (1969) 6 (2): 161–183.
Published: 01 May 1969
..., Series A , 26 , 31 – 38 . Feller W. ( 1941 ). On the integral equation of renewal theory . Annals Math. Stat. , 12 , 243 – 267 . 10.1214/aoms/1177731708 FeIler W. ( 1948 ). On probability problems in the theory of counters Courant Anniversary Volume . New York...
Journal Article
Demography (1987) 24 (3): 431–438.
Published: 01 August 1987
.... , & Arthur , W. B. ( 1982 ). Immigration and the stable population model . Demography , 19 , 125 – 133 . 10.2307/2061132 Feller , W. ( 1941 ). On the integral equation of renewal theory . Annals of Mathematical Statistics , 12 , 243 – 267 . 10.1214/aoms/1177731708 Langhar...
Journal Article
Demography (1987) 24 (4): 443–465.
Published: 01 November 1987
... . 10.2307/3145654 Stys , W. ( 1957 ). The influence of economic conditions on the fertility of peasant women . Population Studies , 11 , 136 – 136 . 10.2307/2172109 Tuljapurkar, S. In press. Cycles in nonlinear age-structured models I: Renewal equations. Theoretical Population...
Journal Article
Demography (1997) 34 (4): 551–563.
Published: 01 November 1997
... Let the age-specific fertility function be characterized by m(a,e). m is affected by e such that om(a,e)/oe 0 Va and THE DYNAMICS OF THE AGE DISTRIBUTION Background and Notations Consider the renewal equation for the case of fixed age-spe- cific rates. Let B(t) be the births at instant t, lea...
Journal Article
Demography (1984) 21 (1): 109–128.
Published: 01 February 1984
..." of the change itself (first term on the right). The perturbation SB is thus given by a Lotka-type renewal equation with a nonhomogeneous or forcing term." Temporal changes in the age pattern of fertility, we can conclude, change the age composition in two stages. They alter first the birth sequence, according...
Journal Article
Demography (1983) 20 (3): 285–298.
Published: 01 August 1983
..., matrix equation formulation (Leslie, 1945). In either case, Renewal Theory is mathematically "exact" in the sense that it contains no intentional approximation. Thus, if all mathematical functions which serve as input to the model are provided exactly, the output of the model-the birth trajec- tory...
Journal Article
Demography (1979) 16 (4): 575–601.
Published: 01 November 1979
...; this section shows how the classi- cal demographic deterministic models can be integrated within this system and illus- trates the analysis by reference to the problem of forecasting births. The classical renewal equation for a closed population (see, for example, Saboia [1977]) is given by b, = /JrPt-l...