Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Brownian-Time Processes: The PDE Connection and the Half-Derivative
  Generator   We introduce a class of interesting stochastic processes based on
Brownian-time processes. These are obtained by taking Markov processes and
replacing the time parameter with the modulus of Brownian motion. They
generalize the iterated Brownian motion (IBM) of Burdzy and the Markov snake of
Le Gall, and they introduce new interesting examples. After defining
Brownian-time processes, we relate them to fourth order parabolic PDEs. We then
study their exit problem as they exit nice domains in $\Rd$, and connect it to
elliptic PDEs. We show that these processes have the peculiar property that
they solve fourth order parabolic PDEs, but their exit distribution - at least
in the standard Brownian-time process case - solves the usual second order
Dirichlet problem. We recover fourth order PDEs in the elliptic setting by
encoding the iterative nature of the Brownian-time process, through its exit
time, in a standard Brownian motion. We also show that it is possible to assign
a formal generator to these non-Markovian processes by giving such a generator
in the half-derivative sense.

10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat