Skorokhod's M1 topology for distribution-valued processes

Skorokhod's M1 topology is defined for c\`adl\`ag paths taking values in the space of tempered distributions (more generally, in the dual of a countably Hilbertian nuclear space). Compactness and tightness characterisations are derived which allow us to study a collection of stochastic processes through their projections on the familiar space of real-valued c\`adl\`ag processes. It is shown how this topological space can be used in analysing the convergence of empirical process approximations to distribution-valued evolution equations with Dirichlet boundary conditions.Comment: 13 pages, 2 figure

From Queen Caroline to Lady Dedlock: Dickens and the popular radical imagination

On an autumn day in 1842, William Hone lay dying. He was by now an obscure figure, but through the services of an old friend, George Cruikshank, he sent a request to Charles Dickens that he might shake his hand before he died. The famous novelist agreed to the request, and for a brief moment Dickens, Cruikshank, and William Hone came together in Hone's shabby London home. The meeting apparently meant little to Dickens who, subsequently attending Hone's funeral, recounted with comic viciousness Cruikshank's histrionics as his old friend was laid to rest. Writing to an American friend, Cornelius Felton, Dickens described how he found himself “almost sobbing with laughter at the funereal absurdities of George Cruikshank and others” (Ackroyd 407). The encounter between Dickens, Cruikshank, and Hone in 1842 is a little-known but with hindsight a significant convergence; for despite Dickens's seeming disregard for the ailing and rather threadbare old bookseller, the deathbed tableau crystallizes an important and much overlooked connection between Dickens's writings and an earlier popular radical tradition.

Funds of Funds: A Closer Look at Age-Based Investing

Over the next 20 years, 76 million Americans born between 1946 and 1964 will hit the half-century mark. For most, this means facing up to the hard questions of how, or even if, they will be able to afford retirement. Only 40% of Americans feel as if their retirement investment vehicles are adequately funded. A major problem with the inadequate funding of the other 60% of these individuals’ portfolios is the fact that they are not capturing potential returns due to their failure to properly diversify among different asset classes. Over the last decade, mutual fund companies have recognized this significant business opportunity and have begun to tailor funds that target retirees specifically. Companies now offer products that give clients a one ticket diversification solution providing retirement income at a later date, usually indicated by the funds name; for example, Target Retirement 2040. These mutual funds are inherently funds of funds that pursue their investment objective by investing in other mutual funds rather than individually picking stocks and bonds. Life-cycle funds, primarily sold through 401(k)s, are designed to offer a riskier asset allocation in early years and then become more conservative as the investor’s target retirement date comes closer. The retirement funds industry has been growing rapidly with assets under management increasing exponentially. This growth is partly explained by the Pension Protection Act, passed this past year, which automatically helps employers to enroll employees in retirement plans. The law also makes it easier to designate life-cycle funds as default investments in retirement plans

A McKean--Vlasov equation with positive feedback and blow-ups

We study a McKean--Vlasov equation arising from a mean-field model of a particle system with positive feedback. As particles hit a barrier they cause the other particles to jump in the direction of the barrier and this feedback mechanism leads to the possibility that the system can exhibit contagious blow-ups. Using a fixed-point argument we construct a differentiable solution up to a first explosion time. Our main contribution is a proof of uniqueness in the class of c\`{a}dl\`{a}g functions, which confirms the validity of related propagation-of-chaos results in the literature. We extend the allowed initial conditions to include densities with any power law decay at the boundary, and connect the exponent of decay with the growth exponent of the solution in small time in a precise way. This takes us asymptotically close to the control on initial conditions required for a global solution theory. A novel minimality result and trapping technique are introduced to prove uniqueness.Comment: 34 pages, 5 figure

Shieling activity in the Norse Eastern Settlement : palaeoenvironment of the 'Mountain Farm', Vatnahverfi, Greenland

Peer reviewedPostprin

The biogeographical status of Alnus crispa (Ait.) Pursch in sub-Arctic southern Greenland : Do pollen records indicate local populations during the past 1500 years?

The Leverhulme Trust is thanked for financial support. We also thank the referees for their constructive comments that helped to improve the paper.Peer reviewedPostprin

A multiple profile approach to the palynological reconstruction of Norse landscapes in Greenland's Eastern Settlement

Acknowledgments The Leverhulme Trust is thanked for financial support. Gordon Cook provided radiocarbon dates. Thanks are also due to Andy McMullen for botanical identifications and assistance in the field, and to Sikuu Motzfeld for hospitality during fieldwork. We are also grateful to Emilie Gauthier, Mike Kaplan, Pete Langdon and Alan Gillespie for their comments.Peer reviewedPostprin

Competing hypotheses, ordination and pollen preservation : landscape impacts of Norse landnám in southern Greenland

We thank the Leverhulme Trust for financial support, and Gordon Cook and staff at SUERC for the provision of radiocarbon dates. We are grateful to two anonymous reviewers and Shinya Sugita for valuable comments which improved the manuscript.Peer reviewedPostprin