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For a Brownian bridge from 0 to y, we prove that the mean of the first exit time from the interval
$\left( -h,h \right),h>0$
, behaves as
. Similar behaviour is also seen to hold for the three-dimensional Bessel bridge. For the Brownian bridge and three-dimensional Bessel bridge, this mean of the first exit time has a puzzling representation in terms of the Kolmogorov distribution. The result regarding the Brownian bridge is applied to provide a detailed proof of an estimate needed by Walsh to determine the convergence of the binomial tree scheme for European options.
We used fossil Chironomidae assemblages and the transfer function approach to reconstruct summer air temperatures over the past 300 years from a High Arctic lake in Hornsund, Svalbard. Our aims were to compare reconstructed summer temperatures with observed (last 100 years) seasonal temperatures, to determine a potential climate warming break point in the temperature series and to assess the significance and rate of the climate warming trend at the study site. The reconstructed temperatures were consistent with a previous proxy record from Svalbard and showed good correlation with the meteorological observations from Bjørnøya and Longyearbyen. From the current palaeoclimate record, we found a significant climate warming threshold in the 1930s, after which the temperatures rapidly increased. We also found that the climate warming trend was strong and statistically significant. Compared with the reconstructed Little Ice Age temperatures in late eighteenth century cooling culmination, the present day summer temperatures are >4°C higher and the temperature increase since the 1930s has been 0.5°C per decade. These results highlight the exceptionally rapid recent warming of southern Svalbard and add invaluable information on the seasonality of High Arctic climate change and Arctic amplification.
The aims of this study were to investigate the consistency of use of plant stanol ester margarine and to characterise consistent and inconsistent users.
A cohort of plant stanol ester margarine users was established based on 14 national surveys conducted by the National Public Health Institute in Finland between 1996 and 1999. A follow-up study questionnaire was developed and sent to 1294 users in 2000.
Subjects who reported using plant stanol ester margarine in both the original survey and the follow-up study were classified as consistent users, and the rest as inconsistent users.
The study population consisted of 1094 subjects aged 18–87 years, 590 men and 504 women.
There were 357 (33%) consistent and 737 (67%) inconsistent users of plant stanol ester margarine in the study population. Consistent users were more likely to be men and to have a higher household income than inconsistent users. Both consistent and inconsistent users were predominantly middle-aged persons with a healthy lifestyle and diet as well as a history of cardiovascular disease. Healthfulness was the main factor affecting bread spread choice among 94% of the consistent users and 59% of the inconsistent users.
The use of plant stanol ester margarine is more often inconsistent than consistent. There is nevertheless a relatively large subgroup of long-term users of plant stanol ester margarine. It is important to examine the health effects especially among these regular users.
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