Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Differential Equations: A Wiener Chaos Approach   A new method is described for constructing a generalized solution for
stochastic differential equations. The method is based on the Cameron-Martin
version of the Wiener Chaos expansion and provides a unified framework for the
study of ordinary and partial differential equations driven by finite- or
infinite-dimensional noise with either adapted or anticipating input.
Existence, uniqueness, regularity, and probabilistic representation of this
Wiener Chaos solution is established for a large class of equations. A number
of examples are presented to illustrate the general constructions. A detailed
analysis is presented for the various forms of the passive scalar equation and
for the first-order It\^{o} stochastic partial differential equation.
Applications to nonlinear filtering if diffusion processes and to the
stochastic Navier-Stokes equation are also discussed.

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con