Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Backward stochastic differential equations with time delayed generators
  - results and counterexamples   We deal with backward stochastic differential equations with time delayed
generators. In this new type of equations, a generator at time t can depend on
the values of a solution in the past, weighted with a time delay function for
instance of the moving average type. We prove existence and uniqueness of a
solution for a sufficiently small time horizon or for a sufficiently small
Lipschitz constant of a generator. We give examples of BSDE with time delayed
generators that have multiple solutions or that have no solutions. We show for
some special class of generators that existence and uniqueness may still hold
for an arbitrary time horizon and for arbitrary Lipschitz constant. This class
includes linear time delayed generators, which we study in more detail. We are
concerned with different properties of a solution of a BSDE with time delayed
generator, including the inheritance of boundedness from the terminal
condition, the comparison principle, the existence of a measure solution and
the BMO martingale property. We give examples in which they may fail.

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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph