Approximation of SDE solutions using local asymptotic expansions

The diffusion approximation in neutron transport theory – asymptotic expansions

Asymptotic Expansions

Asymptotic expansions of functions are useful in statistics in three main ways. Firstly, conventional asymptotic expansions of special functions are useful for approximate computation of integrals arising in statistical calculations. An example given below is the use of Stirling's approximation to the gamma function. Second, asymptotic expansions of density or distribution functions of estimato...

Weak Approximation of a Fractional Sde

Abstract. In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H ∈ (1/3, 1/2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process studied in [4, 7], and our method of proof relies on the algebraic integration theory introduced by Gubinelli in [13].

Weak Approximation of a Fractional Sde

After a decade of efforts [2, 5, 9, 15, 16, 20, 21], it can arguably be said that the basis of the stochastic integration theory with respect to a rough path in general, and with respect to a fractional Brownian motion (fBm in the sequel) in particular, has been now settled in a rather simple and secure way. This allows in particular to define rigorously and solve equations on an arbitrary inte...

Asymptotic Expansions Methodsand Applications

Feynman diagrams are the most important theoretical tool for particle physicists. They are an efficient link between theory and experiment. However, their translation into actual numerical predictions is often very tedious if not impossible. Huge efforts have been devoted to their evaluation, and several powerful methods have been developed to systemize their treatment. The more complex a Feynm...