Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-step Richardson-Romberg Extrapolation: Remarks on Variance Control
  and complexity   We propose a multi-step Richardson-Romberg extrapolation method for the
computation of expectations $E f(X_{_T})$ of a diffusion $(X_t)_{t\in [0,T]}$
when the weak time discretization error induced by the Euler scheme admits an
expansion at an order $R\ge 2$. The complexity of the estimator grows as $R^2$
(instead of $2^R$) and its variance is asymptotically controlled by considering
some consistent Brownian increments in the underlying Euler schemes. Some Monte
carlo simulations carried with path-dependent options (lookback, barriers)
which support the conjecture that their weak time discretization error also
admits an expansion (in a different scale). Then an appropriate
Richardson-Romberg extrapolation seems to outperform the Euler scheme with
Brownian bridge.

1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con