Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sample-Path Equivalent CM Models   The conditionally Markov (CM) sequence contains different classes including
Markov, reciprocal, and so-called $CM_L$ and $CM_F$ (two special classes of CM
sequences). Each class has its own forward and backward dynamic models. The
evolution of a CM sequence can be described by different models. For example, a
Markov sequence can be described by a Markov model, as well as by reciprocal,
$CM_L$, and $CM_F$ models. Also, sometimes a forward model is available, but it
is desirable to have a backward model for the same sequence (e.g., in
smoothing). Therefore, it is important to study relationships between different
dynamic models of a CM sequence. This paper discusses such relationships
between models of nonsingular Gaussian (NG) $CM_L$, $CM_F$, reciprocal, and
Markov sequences. Two models are said to be explicitly sample-equivalent if not
only they govern the same sequence, but also a one-one correspondence between
their sample paths is made explicitly. A unified approach is presented, such
that given a forward/backward $CM_L$/$CM_F$/reciprocal/Markov model, any
explicitly equivalent model can be obtained. As a special case, a backward
Markov model explicitly equivalent to a given forward Markov model can be
obtained regardless of the singularity/nonsingularity of the state transition
matrix of the model.

31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: acc-phys