Modeling quantum measurement probability as a classical stochastic process

Chaos

Volumn 11, Issue 3, 2001, Pages 548-562

  Gillespie, Daniel T ^a   Alltop, William O ^a   Martin, Jorge M ^a  

^a NAVAL AIR WARFARE CENTER   (United States)

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EID: 0035458183     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1378791     Document Type: Article

References (21)

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14. 1), for all real α, and with Eq. (9a) duly satisfied. But none of these solutions can claim to be probabilities since they stray outside the unit interval. More surprisingly, none of these solutions satisfies (identically) the Chapman-Kolmogorov equation (7). We suspect that requiring W to be non-negative might ensure that solutions to Eq. (10) will be genuine probabilities obeying Eq. (7), but we are unaware of any proven theorem to that effect.
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18. 1), for all k ≥ 1 and n ≥ 1, of which the set (13) is the k = 1 subset; however, as is explained in Refs. 14-16, that doubly infinite set is completely and uniquely determined by the subset (13).
19. 1." The practical effect of this constraint which is imposed by classical stochastic process theory on our analysis is simply this: For any t′ > t, P(x′,t′|x,t) is to be evaluated using formulas (27a) and (27b). And this will be so even in the non-Markovian case.
20. We have learned through a private communication that the one-jump-percycle process W functions (38a) and (38b) were discovered earlier, in a different context, by H. Wiseman (unpublished).
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