Abstract
This note will remove some unnecessary regularity assumptions from my first paper on the subject [1]. There, beyond the conditions of spatial and temporal homogeneity, Lorentz-invariance, the Markov property, and the requirement that speeds be less than that of light, there were additional assumptions: continuity in probability ((E), p. 248) and existence of derivatives with probability one at each time (first half of (C), p. 248). Both these assumptions will be shown to follow from the others. This makes easier the proof of the converse part of the main theorem of [1], Theorem 8.2, as will be indicated below.
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Dudley, R. M., Lorentz-invariant Markov processes in relativistic phase space, Arkiv för Matematik 6, 241–268 (1965).
Dynkin, E. B., Theory of Markov Processes (Moscow, 1959; English translation, London, Pergamon, 1960).
Dynkin, E. B., Markov Processes (Moscow, 1963; English translation, Berlin, Springer, 1965).
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Dudley, R.M. (2010). A note on Lorentz-invariant Markov processes. In: Giné, E., Koltchinskii, V., Norvaisa, R. (eds) Selected Works of R.M. Dudley. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5821-1_8
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DOI: https://doi.org/10.1007/978-1-4419-5821-1_8
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