A Girsanov transformation for birth and death on a Brownian flow

1996 ◽  
Vol 33 (1) ◽  
pp. 88-100 ◽  
Author(s):  
Michael J. Phelan
Keyword(s):  
Spatial Configuration ◽  
Particle System ◽  
Continuous Change ◽  
Drift Diffusion ◽  
Absolutely Continuous ◽  
Death Rates ◽  
Girsanov Transformation ◽  
Girsanov Formula ◽  
System Of Particles ◽  
Particle Process

We consider a system of particles in birth and death on a Brownian flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of counting measures. The system depends on a handful of parameters including a rate of drift, diffusion, birth, and killing. We exhibit a Girsanov formula for the absolutely continuous change of particle system by way of a change of drift, birth, and killing rates. We can only allow for a restrictive change of drift on the flow, but for fairly unrestrictive change of birth and death rates. The result is therefore of some interest in problems of statistical inference from passive transport of transient tracers.

A Girsanov transformation for birth and death on a Brownian flow

1996 ◽  
Vol 33 (01) ◽  
pp. 88-100
Author(s):  
Michael J. Phelan
Keyword(s):  
Spatial Configuration ◽  
Particle System ◽  
Continuous Change ◽  
Drift Diffusion ◽  
Absolutely Continuous ◽  
Death Rates ◽  
Girsanov Transformation ◽  
Girsanov Formula ◽  
System Of Particles ◽  
Particle Process

We consider a system of particles in birth and death on a Brownian flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of counting measures. The system depends on a handful of parameters including a rate of drift, diffusion, birth, and killing. We exhibit a Girsanov formula for the absolutely continuous change of particle system by way of a change of drift, birth, and killing rates. We can only allow for a restrictive change of drift on the flow, but for fairly unrestrictive change of birth and death rates. The result is therefore of some interest in problems of statistical inference from passive transport of transient tracers.

Birth and death on a Brownian flow: a Feller semigroup and its generator and a martingale problem

1996 ◽  
Vol 33 (01) ◽  
pp. 71-87 ◽  
Author(s):  
Michael J. Phelan
Keyword(s):  
Markov Process ◽  
Spatial Configuration ◽  
Martingale Problem ◽  
Stochastic Flow ◽  
Transition Semigroup ◽  
Feller Semigroup ◽  
System Of Particles ◽  
Particle Process

We consider a system of particles in birth and death on a stochastic flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of bounded counting measures. We show that its transition semigroup is a Feller semigroup and exhibit its pregenerator. The pregenerator defines a martingale problem. We show that the particle process solves the problem uniquely.

Birth and death on a Brownian flow: a Feller semigroup and its generator and a martingale problem

1996 ◽  
Vol 33 (1) ◽  
pp. 71-87 ◽  
Author(s):  
Michael J. Phelan
Keyword(s):  
Markov Process ◽  
Spatial Configuration ◽  
Martingale Problem ◽  
Stochastic Flow ◽  
Transition Semigroup ◽  
Feller Semigroup ◽  
System Of Particles ◽  
Particle Process

We consider a system of particles in birth and death on a stochastic flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of bounded counting measures. We show that its transition semigroup is a Feller semigroup and exhibit its pregenerator. The pregenerator defines a martingale problem. We show that the particle process solves the problem uniquely.

scholarly journals The impact of violence on Venezuelan life expectancy and lifespan inequality

2019 ◽  
Vol 48 (5) ◽  
pp. 1593-1601 ◽  
Author(s):  
Jenny García ◽  
José Manuel Aburto
Keyword(s):  
Life Expectancy ◽  
Causes Of Death ◽  
Change Model ◽  
Continuous Change ◽  
Age At Death ◽  
Mortality Trends ◽  
Death Rates ◽  
Specific Mortality ◽  
The Impact ◽  
Mortality Estimates

Abstract Background Venezuela is one of the most violent countries in the world. According to the United Nations, homicide rates in the country increased from 32.9 to 61.9 per 100 000 people between 2000 and 2014. This upsurge coincided with a slowdown in life expectancy improvements. We estimate mortality trends and quantify the impact of violence-related deaths and other causes of death on life expectancy and lifespan inequality in Venezuela. Methods Life tables were computed with corrected age-specific mortality rates from 1996 to 2013. From these, changes in life expectancy and lifespan inequality were decomposed by age and cause of death using a continuous-change model. Lifespan inequality, or variation in age at death, is measured by the standard deviation of the age-at-death distribution. Results From 1996 to 2013 in Venezuela, female life expectancy rose 3.57 [95% confidence interval (CI): 3.08–4.09] years [from 75.79 (75.98–76.10) to 79.36 (78.97–79.68)], and lifespan inequality fell 1.03 (–2.96 to 1.26) years [from 18.44 (18.01–19.00) to 17.41 (17.30–18.27)]. Male life expectancy increased 1.64 (1.09–2.25) years [from 69.36 (68.89–59.70) to 71.00 (70.53–71.39)], but lifespan inequality increased 0.95 (–0.80 to 2.89) years [from 20.70 (20.24–21.08) to 21.65 (21.34–22.12)]. If violence-related death rates had not risen over this period, male life expectancy would have increased an additional 1.55 years, and lifespan inequality would have declined slightly (–0.31 years). Conclusions As increases in violence-related deaths among young men (ages 15–39) have slowed gains in male life expectancy and increased lifespan inequality, Venezuelan males face more uncertainty about their age at death. There is an urgent need for more accurate mortality estimates in Venezuela.

scholarly journals On absolutely continuous change of measure and Markov property of stochastic processes

1969 ◽  
Vol 9 (1) ◽  
pp. 57-71
Author(s):  
B. Grigelionis
Keyword(s):  
Stochastic Processes ◽  
Markov Property ◽  
Continuous Change ◽  
Change Of Measure ◽  
Absolutely Continuous

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Б. Григелионис. Об абсолютно непрерывной замене меры и марковском свойстве случайных процессов B. Grigelionis. Apie absoliučiai tolydinį mato pakeitimą ir atsitiktinių procesų Markovo savybę

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