Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the conditional joint probability distributions of phase-type under
  the mixture of finite-state absorbing Markov jump processes   This paper presents some new results on the conditional joint probability
distributions of phase-type under the mixture of right-continuous Markov jump
processes with absorption on the same finite state space $\mathbb{S}$ moving at
different speeds, where the mixture occurs at a random time. Such mixture was
first proposed by Frydman \cite{Frydman2005} and Frydman and Schuermann
\cite{Frydman2008} as a generalization of the mover-stayer model of Blumen et
at. \cite{Blumen}, and was recently extended by Surya \cite{Surya2018}. When
conditioning on all previous and current information
$\mathcal{F}_{t,i}=\mathcal{F}_{t-}\cup\{X_t=i\}$, with
$\mathcal{F}_{t-}=\{X_s, 0<s\leq t-\}$ and $i\in\mathbb{S}$, of the mixture
process $X$, distributional identities are explicit in terms of the Bayesian
updates of switching probability, the likelihoods of observing the sample
paths, and the intensity matrices of the underlying Markov processes, despite
the fact that the mixture itself is non-Markov. They form non-stationary
function of time and have the ability to capture heterogeneity and path
dependence. When the underlying processes move at the same speed, in which case
the mixture reduces to a simple Markov jump process, these features are
removed, and the distributions coincide with that of given by Neuts
\cite{Neuts1975} and Assaf et al. \cite{Assaf1984}. Furthermore, when
conditioning on $\mathcal{F}_{t-}$ and no exit to the absorbing set has been
observed at time $t$, the distributions are given explicitly in terms of an
additional Bayesian updates of probability distribution of $X$ on $\mathbb{S}$.
Examples are given to illustrate the main results.

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The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat