Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bounds for the density of locally elliptic It\^{o} processes   We give lower bounds for the density $p_T(x,y)$ of the law of $X_t$, the
solution of $dX_t=\sigma (X_t) dB_t+b(X_t) dt,X_0=x,$ under the following local
ellipticity hypothesis: there exists a deterministic differentiable curve $x_t,
0\leq t\leq T$, such that $x_0=x, x_T=y$ and $\sigma \sigma ^*(x_t)>0,$ for all
$t\in \lbrack 0,T].$ The lower bound is expressed in terms of a distance
related to the skeleton of the diffusion process. This distance appears when we
optimize over all the curves which verify the above ellipticity assumption. The
arguments which lead to the above result work in a general context which
includes a large class of Wiener functionals, for example, It\^{o} processes.
Our starting point is work of Kohatsu-Higa which presents a general framework
including stochastic PDE's.

18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int