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An Elementary Proof that the First Hitting Time of an Open Set by a Jump Process is a Stopping Time

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 2078)

Abstract

We give a short and elementary proof that the first hitting time of an open set by the jump process of a càdlàg adapted process is a stopping time.

Keywords

  • Jump Process
  • Elementary Result
  • Elementary Proof
  • Density Property
  • Countable Sequence

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References

  1. R.F. Bass, The measurability of hitting times. Electron. Comm. Probab. 15, 99–105 (2010)

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  2. R.F. Bass, Correction to “The measurability of hitting times”. Electron. Comm. Probab. 16, 189–191 (2011)

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  3. C. Dellacherie, P.-A. Meyer, Probabilities and Potential. North-Holland Mathematics Studies, vol. 29 (North-Holland, Amsterdam, 1978)

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  4. P. Protter, Stochastic Integration and Differential Equations, 2nd edn. Version 2.1. Stochastic Modelling and Applied Probability, vol. 21 (Springer, Berlin, 2005)

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  5. L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, 2nd edn., vol. 1 (Cambridge University Press, Cambridge, 2000)

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Correspondence to Alexander Sokol .

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© 2013 Springer International Publishing Switzerland

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Sokol, A. (2013). An Elementary Proof that the First Hitting Time of an Open Set by a Jump Process is a Stopping Time. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLV. Lecture Notes in Mathematics(), vol 2078. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00321-4_11

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