Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Most Probable Transition Paths of Stochastic Dynamical Systems:
  Equivalent Description and Characterization   This work is devoted to show a sufficient and necessary description for the
most probable transition paths of stochastic dynamical systems with Brownian
noise. The equivalence is established by studying the relations between
Markovian bridge measures and the Onsgaer-Machlup action functional. This
cannot be achieved by existing methods because Markovian bridge measures are
not quasi translation invariant. We overcome this problem by showing that the
Onsager-Machlup action functional can be derived from a Markovian bridge
process. We then demonstrate that, for some special cases of which one is a
class of linear stochastic systems and another is a class of nonlinear
stochastic systems with small noise, the most probable transition path can be
determined by a first order deterministic differential equation with an initial
value.Finally, we illustrate our results with several examples.

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The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th