Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The optimal free knot spline approximation of stochastic differential
  equations with additive noise   In this paper we analyse the pathwise approximation of stochastic
differential equations by polynomial splines with free knots. The pathwise
distance between the solution and its approximation is measured globally on the
unit interval in the $L_{\infty}$-norm, and we study the expectation of this
distance. For equations with additive noise we obtain sharp lower and upper
bounds for the minimal error in the class of arbitrary spline approximation
methods, which use $k$ free knots. The optimal order is achieved by an
approximation method $\hat{X}_{k}^{\dagger}$, which combines an Euler scheme on
a coarse grid with an optimal spline approximation of the Brownian motion $W$
with $k$ free knots.

5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin