Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Perron's method and elementary strategies for zero-sum
  differential games   We develop here the Stochastic Perron Method in the framework of two-player
zero-sum differential games. We consider the formulation of the game where both
players play, symmetrically, feed-back strategies (as in [CR09] or [PZ12]) as
opposed to the Elliott-Kalton formulation prevalent in the literature. The
class of feed-back strategies we use is carefully chosen so that the state
equation admits strong solutions and the technicalities involved in the
Stochastic Perron Method carry through in a rather simple way. More precisely,
we define the game over elementary strategies, which are well motivated by
intuition. Within this framework, the Stochastic Perron Method produces a
viscosity sub-solution of the upper Isaacs equation dominating the upper value
of the game, and a viscosity super-solution of the upper Isaacs equation lying
below the upper value of the game. Using a viscosity comparison result we
obtain that the upper value is the unique and continuous viscosity solution of
the upper Isaacs equation. An identical statement holds for the lower value and
lower Isaacs equation. A version of the Dynamic Programming Principle is
obtained as a by-product. If the Isaacs condition holds, the game has a value
over elementary (pure) strategies.

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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio