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- Andersen, Lars Norvang, et al.
(author)
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Levy Processes with Two-Sided Reflection
- 2015
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In: Lecture Notes in Mathematics. - Cham : Springer International Publishing. - 0075-8434. ; 2149, s. 67-182
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Journal article (peer-reviewed)abstract
- Let X be a Levy process and V the reflection at boundaries 0 and b > 0. A number of properties of V are studied, with particular emphasis on the behaviour at the upper boundary b. The process V can be represented as solution of a Skorokhod problem V(t) = V(0)+X(t)+L(t)-U(t) where L, U are the local times (regulators) at the lower and upper barrier. Explicit forms of V in terms of X are surveyed as well as more pragmatic approaches to the construction of V, and the stationary distribution pi is characterised in terms of a two-barrier first passage problem. A key quantity in applications is the loss rate l(b) at b, defined as E-pi U(1). Various forms of l(b) and various derivations are presented, and the asymptotics as b -> infinity is exhibited in both the light-tailed and the heavy-tailed regime. The drift zero case EX(1) = 0 plays a particular role, with Brownian or stable functional limits being a key tool. Further topics include studies of the first hitting time of b, central limit theorems and large deviations results for U, and a number of explicit calculations for Levy processes where the jump part is compound Poisson with phase-type jumps.
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2. |
- Seror, Raphaèle, et al.
(author)
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EULAR Sjögren's syndrome disease activity index (ESSDAI): a user guide.
- 2015
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In: RMD Open. - : BMJ. - 2056-5933. ; 1:1, s. 000022-000022
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Research review (peer-reviewed)abstract
- The EULAR Sjögren's syndrome (SS) disease activity index (ESSDAI) is a systemic disease activity index that was designed to measure disease activity in patients with primary SS. With the growing use of the ESSDAI, some domains appear to be more challenging to rate than others. The ESSDAI is now in use as a gold standard to measure disease activity in clinical studies, and as an outcome measure, even a primary outcome measure, in current randomised clinical trials. Therefore, ensuring an accurate and reproducible rating of each domain, by providing a more detailed definition of each domain, has emerged as an urgent need. The purpose of the present article is to provide a user guide for the ESSDAI. This guide provides definitions and precisions on the rating of each domain. It also includes some minor improvement of the score to integrate advance in knowledge of disease manifestations. This user guide may help clinicians to use the ESSDAI, and increase the reliability of rating and consequently of the ability to detect true changes over time. This better appraisal of ESSDAI items, along with the recent definition of disease activity levels and minimal clinically important change, will improve the assessment of patients with primary SS and facilitate the demonstration of effectiveness of treatment for patients with primary SS.
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