Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The H\"ormander condition for delayed stochastic differential equations   In this paper, we are interested in path-dependent stochastic differential
equations (SDEs) which are controlled by Brownian motion and its delays. Within
this non-Markovian context, we give a H \"ormander-type criterion for the
regularity of solutions. Indeed, our criterion is expressed as a spanning
condition with brackets. A novelty in the case of delays is that noise can
"flow from the past" and give additional smoothness thanks to semi-brackets.
  The proof follows the general lines of Malliavin's probabilistic proof, in
the Markovian case. Nevertheless, in order to handle the non-Markovian aspects
of this problem and to treat anticipative integrals in a path-wise fashion, we
heavily invoke rough path integration.

36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex