Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: pth moment noise-to-state stability of stochastic differential equations
  with persistent noise   This paper studies the stability properties of stochastic differential
equations subject to persistent noise (including the case of additive noise),
which is noise that is present even at the equilibria of the underlying
differential equation and does not decay with time. The class of systems we
consider exhibit disturbance attenuation outside a closed, not necessarily
bounded, set. We identify conditions, based on the existence of Lyapunov
functions, to establish the noise-to-state stability in probability and in pth
moment of the system with respect to a closed set. As part of our analysis, we
study the concept of two functions being proper with respect to each other
formalized via a pair of inequalities with comparison functions. We show that
such inequalities define several equivalence relations for increasingly strong
refinements on the comparison functions. We also provide a complete
characterization of the properties that a pair of functions must satisfy to
belong to the same equivalence class. This characterization allows us to
provide checkable conditions to determine whether a function satisfies the
requirements to be a strong NSS-Lyapunov function in probability or a pth
moment NSS-Lyapunov function. Several examples illustrate our results.

37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom