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- Andersen, Lars Norvang, et al.
(författare)
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Levy Processes with Two-Sided Reflection
- 2015
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Ingår i: Lecture Notes in Mathematics. - Cham : Springer International Publishing. - 0075-8434. ; 2149, s. 67-182
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Tidskriftsartikel (refereegranskat)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. |
- Glynn, Liam, et al.
(författare)
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The Limerick Declaration on Rural Health Care 2022
- 2023
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Ingår i: Rural and Remote Health. - 1445-6354. ; 23:1, s. 7905-7905
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Tidskriftsartikel (refereegranskat)abstract
- The 19th World Rural Health Conference, hosted in rural Ireland and the University of Limerick, with over 650 participants coming from 40 countries and an additional 1600 engaging online, has carefully considered how best rural communities can be empowered to improve their own health and the health of those around them. The conference also considered the role of national health systems and all stakeholders, in keeping with the commitments made through the Sustainable Development Goals and the enjoyment of the highest attainable standard of health as one of the fundamental rights of every human being. This conference declaration, the Limerick Declaration on Rural Healthcare, is designed to inform rural communities, academics and policymakers about how to achieve the goal of delivering high quality health care in rural and remote areas most effectively, with a particular focus on the Irish healthcare system. Congruent with current evidence and best international practice, the participants of the conference endorsed a series of recommendations for the creation of high quality, sustainable and cost-effective healthcare delivery for rural communities in Ireland and globally. The recommendations focused on four major themes: rural healthcare needs and delivery, rural workforce, advocacy and policy, and research for rural health care. Equal access to health care is a crucial marker of democracy. Hence, we call on all governments, policymakers, academic institutions and communities globally to commit to providing their rural dwellers with equitable access to health care that is properly resourced and fundamentally patient-centred in its design.
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3. |
- Pihlsgård, Mats, et al.
(författare)
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On the Dynamics of Semimartingales with Two Reflecting Barriers
- 2013
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Ingår i: Journal of Applied Probability. - 1475-6072. ; 50:3, s. 671-685
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Tidskriftsartikel (refereegranskat)abstract
- We consider a semimartingale X which is reflected at an upper barrier T and a lower barrier S, where S and T are also semimartingales such that T is bounded away from S. First, we present an explicit construction of the reflected process. Then we derive a relationship in terms of stochastic integrals linking the reflected process and the local times at the respective bathers to X, S, and T. This result reveals the fundamental structural properties of the reflection mechanism. We also present a few results showing how the general relationship simplifies under additional assumptions on X, S, and T, e.g. if we take X, S, and T to be independent martingales (which satisfy some extra technical conditions).
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