Generalized Age-Dependence and Random Characteristics
Søren Asmussen, H. Hering · Birkhäuser Boston eBooks · 1983
Associated with the typical individual of the process is A point process ξ (the reproduction ) on [0,∞) describing the instants of births. That is, ξ(t) is the number of children born before or at age t, EquationSource % MathType!MTEF!2!1!+- % feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdG3aae % WaaeaacaWG0baacaGLOaGaayzkaaGaeyypa0Zaa8qmaeaacqaH+oaE % aSqaaiaaicdaaeaacaWG0baaniabgUIiYdGccaGGBbGaamizaiaado % hacaGGDbaaaa!448A!]] <![CDATA[$$\xi \left( t \right) = \int_0^t \xi [ds]$$. A r.v. τ (not necessarily finite), the lifelength . A collection of [0,∞)-valued stochastic processes EquationSource % MathType!MTEF!2!1!+- % feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq % aHvpGzdaqadaqaaiaadshaaiaawIcacaGLPaaaaiaawIcacaGLPaaa % daWgaaWcbaGaaGimaiabgsMiJkaadshacqGH8aapcqGHEisPaeqaaO % GaaiilamaabmaabaGaeqiYdK3aaeWaaeaacaWG0baacaGLOaGaayzk % aaaacaGLOaGaayzkaaWaaSbaaSqaaiaaicdacqGHKjYOcaWG0bGaey % ipaWJaeyOhIukabeaaaaa!4E6D!]] <![CDATA[$${\left( {\phi \left( t \right)} \right)_{0 \leqslant t < \infty }},{\left( {\psi \left( t \right)} \right)_{0 \leqslant t < \infty }}$$,..., random characteristics .