Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper envelopes of families of Feller semigroups and viscosity solutions
  to a class of nonlinear Cauchy problems   In this paper, we consider the (upper) semigroup envelope, i.e. the least
upper bound, of a given family of linear Feller semigroups. We explicitly
construct the semigroup envelope and show that, under suitable assumptions, it
yields viscosity solutions to abstract Hamilton-Jacobi-Bellman-type partial
differential equations related to stochastic optimal control problems arising
in the field of Robust Finance. We further derive conditions for the existence
of a Markov process under a nonlinear expectation related to the semigroup
envelope for the case where the state space is locally compact. The procedure
is then applied to numerous examples, in particular, nonlinear PDEs that arise
from control problems for infinite dimensional Ornstein-Uhlenbeck and L\'evy
processes.

26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc