Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Backward Stochastic Differential Equations with Markov Chains and The
  Application: Homogenization of PDEs System   Stemmed from the derivation of the optimal control to a stochastic
linear-quadratic control problem with Markov jumps, we study one kind of
backward stochastic differential equations (BSDEs) that the generator f is
affected by a Markovian switching. Then, the case that the Markov chain is
involved in a large state space is considered. Following the classical
approach, a hierarchical approach is adopted to reduce the complexity and a
singularly perturbed Markov chain is involved. We will study the asymptotic
property of BSDE with the singularly perturbed Markov chain. At last, as an
application of our theoretical result, we show the homogenization of one system
of partial differential equations (PDEs) with a singularly perturbed Markov
chain.

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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs