Let h(t) be a smooth function, Bt a standard Brownian motion and th=inf{t;Bt=h(t)} the first hitting time. In this paper, new formulations are derived to evaluate the probability density of the first hitting time. If ...Let h(t) be a smooth function, Bt a standard Brownian motion and th=inf{t;Bt=h(t)} the first hitting time. In this paper, new formulations are derived to evaluate the probability density of the first hitting time. If u(x, t) denotes the density function of x=Bt for t th, then uxx=2ut and u(h(t),t)=0. Moreover, the hitting time density dh(t) is 1/2ux(h(t),t). Applying some partial differential equation techniques, we derive a simple integral equation for dh(t). Two examples are demonstrated in this article.展开更多
For a birth and death processX=|X(t),t <σ| with explosion and lifespanu distributions and joint distributions of first hitting time and first hitting location after explosion of setB n = |0,1,...,n| ,n have been f...For a birth and death processX=|X(t),t <σ| with explosion and lifespanu distributions and joint distributions of first hitting time and first hitting location after explosion of setB n = |0,1,...,n| ,n have been found.展开更多
In Sweden, there has been only limited documentation for injuries requiring ambulance responses. The main objective of this study is, through the use of historic data, to assess the suitability of ambulance records to...In Sweden, there has been only limited documentation for injuries requiring ambulance responses. The main objective of this study is, through the use of historic data, to assess the suitability of ambulance records to describe circumstances with fall injuries. Methods: The injury events data around patients were sourced from the ambulance data register. Descriptive statistics were used to describe injured patients based on age group, type of injury, place of injury, injury mechanism and consequence of an injury event. Two-group comparison was performed with Pearson’s chi-squared. Predictors of transport to hospital were identified using logistic regression analyses. Result: Ambulance provides unique data on all injury events, with direct implications for translational research, public policy and clinical practice (safety promotion). In 2002 ambulance attended 3964 injured people which represents 14% of ambulance attended workload in Värmland county, Sweden. The most common trauma location was the traffic area followed by residential area and nursing home. These three injury sites account for 2320 cases (61.6%). The most common cause of injury was falls (63.9%) followed by contact with another person (26.5%). Contact with another person is the most common site of injury in the traffic area (79.5%), and men aged 25-66 years are overrepresented. Conclusion: Logistic regression found that, age-group and place code were significant predictor for being attended by ambulance. Traffic, home and nursing homes were over-represented injury environments (61.6%) that require special attention. Most injury cases occur in the home and nursing homes among people over 67 years of age. Surprisingly, most of the injury events in the traffic environment are about hitting another person. Paramedics can provide rich and valuable data on injury events. Registration of such data is entirely possible and desirable, and can be used in preventive work.展开更多
文摘Let h(t) be a smooth function, Bt a standard Brownian motion and th=inf{t;Bt=h(t)} the first hitting time. In this paper, new formulations are derived to evaluate the probability density of the first hitting time. If u(x, t) denotes the density function of x=Bt for t th, then uxx=2ut and u(h(t),t)=0. Moreover, the hitting time density dh(t) is 1/2ux(h(t),t). Applying some partial differential equation techniques, we derive a simple integral equation for dh(t). Two examples are demonstrated in this article.
文摘For a birth and death processX=|X(t),t <σ| with explosion and lifespanu distributions and joint distributions of first hitting time and first hitting location after explosion of setB n = |0,1,...,n| ,n have been found.
文摘In Sweden, there has been only limited documentation for injuries requiring ambulance responses. The main objective of this study is, through the use of historic data, to assess the suitability of ambulance records to describe circumstances with fall injuries. Methods: The injury events data around patients were sourced from the ambulance data register. Descriptive statistics were used to describe injured patients based on age group, type of injury, place of injury, injury mechanism and consequence of an injury event. Two-group comparison was performed with Pearson’s chi-squared. Predictors of transport to hospital were identified using logistic regression analyses. Result: Ambulance provides unique data on all injury events, with direct implications for translational research, public policy and clinical practice (safety promotion). In 2002 ambulance attended 3964 injured people which represents 14% of ambulance attended workload in Värmland county, Sweden. The most common trauma location was the traffic area followed by residential area and nursing home. These three injury sites account for 2320 cases (61.6%). The most common cause of injury was falls (63.9%) followed by contact with another person (26.5%). Contact with another person is the most common site of injury in the traffic area (79.5%), and men aged 25-66 years are overrepresented. Conclusion: Logistic regression found that, age-group and place code were significant predictor for being attended by ambulance. Traffic, home and nursing homes were over-represented injury environments (61.6%) that require special attention. Most injury cases occur in the home and nursing homes among people over 67 years of age. Surprisingly, most of the injury events in the traffic environment are about hitting another person. Paramedics can provide rich and valuable data on injury events. Registration of such data is entirely possible and desirable, and can be used in preventive work.
