Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comment on "Why quantum mechanics cannot be formulated as a Markov
  process"   In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607,
(1994)] claims that the theory of Markov stochastic processes cannot provide an
adequate mathematical framework for quantum mechanics. In conjunction with the
specific quantum dynamics considered there, we give a general analysis of the
associated dichotomic jump processes. If we assume that Gillespie's
"measurement probabilities" \it are \rm the transition probabilities of a
stochastic process, then the process must have an invariant (time independent)
probability measure. Alternatively, if we demand the probability measure of the
process to follow the quantally implemented (via the Born statistical
postulate) evolution, then we arrive at the jump process which \it can \rm be
interpreted as a Markov process if restricted to a suitable duration time.
However, there is no corresponding Markov process consistent with the $Z_2$
event space assumption, if we require its existence for all times $t\in R_+$.

16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc