论文标题
在维纳（Wiener）混乱的扩展中
On the Wiener Chaos Expansion of the Signature of a Gaussian Process
论文作者
论文摘要
我们计算了一类高斯过程的签名的Wiener混乱分解，其中包含Brownian Motion（FBM），其中包含Hurst参数H（1/4，1）。在0级，我们的结果对此类过程的预期特征产生了一种表达，这决定了其定律[CL16]。特别是，该公式同时扩展了1/2 <h-fbm [bc07]和布朗运动（H = 1/2）[FAW03]的一个公式，从而解决了一般情况H> 1/4，从而解决了一个既定的开放问题。所研究的其他过程包括连续和中心的高斯半明星。
We compute the Wiener chaos decomposition of the signature for a class of Gaussian processes, which contains fractional Brownian motion (fBm) with Hurst parameter H in (1/4, 1). At level 0, our result yields an expression for the expected signature of such processes, which determines their law [CL16]. In particular, this formula simultaneously extends both the one for 1/2 < H-fBm [BC07] and the one for Brownian motion (H = 1/2) [Faw03], to the general case H > 1/4, thereby resolving an established open problem. Other processes studied include continuous and centred Gaussian semimartingales.
