Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the strong regularity of degenerate additive noise driven stochastic
  differential equations with respect to their initial values   Recently in [M. Hairer, M. Hutzenthaler, and A. Jentzen, Ann. Probab. 43, 2
(2015), 468--527] and [A. Jentzen, T. M\"uller-Gronbach, and L. Yaroslavtseva,
Commun. Math. Sci. 14, 6 (2016), 1477--1500] stochastic differential equations
(SDEs) with smooth coefficient functions have been constructed which have an
arbitrarily slowly converging modulus of continuity in the initial value. In
these SDEs it is crucial that some of the first order partial derivatives of
the drift coefficient functions grow at least exponentially and, in particular,
quicker than any polynomial. However, in applications SDEs do typically have
coefficient functions whose first order partial derivatives are polynomially
bounded. In this article we study whether arbitrarily bad regularity phenomena
in the initial value may also arise in the latter case and we partially answer
this question in the negative. More precisely, we show that every additive
noise driven SDE which admits a Lyapunov-type condition (which ensures the
existence of a unique solution of the SDE) and which has a drift coefficient
function whose first order partial derivatives grow at most polynomially is at
least logarithmically H\"older continuous in the initial value.

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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
8
The categories of this paper are: hep-ex