Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new approach to the existence of invariant measures for Markovian
  semigroups   We give a new, two-step approach to prove existence of finite invariant
measures for a given Markovian semigroup. First, we identify a convenient
auxiliary measure and then we prove conditions equivalent to the existence of
an invariant finite measure which is absolutely continuous with respect to it.
As applications, we give a short proof for the result of Lasota and Szarek on
invariant measures and we obtain a unifying generalization of different
versions for Harris ergodic theorem which provides an answer to an open
question of Tweedie. We show that for a nonlinear SPDE on a Gelfand triple, the
strict coercivity condition is sufficient to guarantee the existence of a
unique invariant probability measure for the associated semigroup, once it
satisfies a Harnack type inequality. A corollary of the main result shows that
any uniformly bounded semigroup on $L^p$ possesses an invariant measures and we
give some applications to sectorial perturbations of Dirichlet forms.

22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci