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2 results

  • 10 - The Condition of Ireland

  • from Part IV - Irish Questions
  • Michael Wheeler, University of Southampton
  • Book:
    The Year That Shaped the Victorian Age
    Published online:
    08 December 2022
    Print publication:
    22 December 2022, pp 312-346

  • Summary

    As we turn to the acute problem of poverty in Ireland and the dominant figure of Daniel O’Connell, the emphasis remains in the public domain. A series of substantial reports, presented in the form of open letters to the editor of The Times, was commissioned by John Thadeus Delane himself. These open letters generated much heat in Irish newspapers, inspired a brilliant parody in Punch and led to the use of a forged private letter by O’Connell’s son, John, in the propaganda war between the Repeal Association and the British establishment. As in the House of Commons, personal honour was at stake when each side challenged the other with regard to accurate reporting. It was Thomas Campbell Foster’s account of ‘The Condition of the People of Ireland’ in The Times that had the greatest impact on the British reading public and that permanently tarnished Daniel O’Connell’s name.

  • On ergodicity and recurrence properties of a Markov chain by an application to an open jackson network

  • Part of
  • Arie Hordijk, Flora Spieksma
  • Journal:
    Advances in Applied Probability / Volume 24 / Issue 2 / June 1992
    Published online by Cambridge University Press:
    01 July 2016, pp. 343-376
    Print publication:
    June 1992

  • This paper gives an overview of recurrence and ergodicity properties of a Markov chain. Two new notions for ergodicity and recurrence are introduced. They are called μ -geometric ergodicity and μ -geometric recurrence respectively. The first condition generalises geometric as well as strong ergodicity. Our key theorem shows that μ -geometric ergodicity is equivalent to weak μ -geometric recurrence. The latter condition is verified for the time-discretised two-centre open Jackson network. Hence, the corresponding two-dimensional Markov chain is μ -geometrically and geometrically ergodic, but not strongly ergodic. A consequence of μ -geometric ergodicity with μ of product-form is the convergence of the Laplace-Stieltjes transforms of the marginal distributions. Consequently all moments converge.