Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Markov processes, polynomial martingales and orthogonal polynomials   We study general properties for the family of stochastic processes with
polynomial regression property, that is that every conditional moment of the
process is a polynomial. It turns out that then there exists a family of
polynomial martingales $\left\{ M_{n}(X_{t},t)\right\}_{n\geq1}$ that contains
complete information on the distribution (both marginal and transitional) of
the process.
  We specify conditions expressed in terms of $M_{n}^{\prime}s$ under which a
given process has independent increments and further is a Levy process,
contains reversed martingales, is a harness or quadratic harness. We also give
conditions under which some of these martingales are also reversed martingales.

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The categories of this paper are: eess
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The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org