论文标题
森林，累积群，烈士
Forests, cumulants, martingales
论文作者
论文摘要
这项工作涉及在过滤概率空间上的一般随机变量的森林和累积类型扩展。我们建立了一个“损坏的指数”扩展，该扩展概括并统一了Al {ò} S，Galedal和Radoičić的指示结果，以及Lacoin，Rhodes和Vargas的累积递归公式。具体而言，我们以前的两个结果表现为同一广义森林扩张的较低维投影，随后通过森林重新排序相关。 Our approach also leads to sharp integrability conditions for validity of the cumulant formula, as required by many of our examples, including iterated stochastic integrals, Lévy area, Bessel processes, KPZ with smooth noise, Wiener-Itô chaos and "rough" stochastic (forward) variance models.
This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability spaces. We establish a "broken exponential martingale" expansion that generalizes and unifies the exponentiation result of Al{ò}s, Gatheral, and Radoičić and the cumulant recursion formula of Lacoin, Rhodes, and Vargas. Specifically, we exhibit the two previous results as lower dimensional projections of the same generalized forest expansion, subsequently related by forest reordering. Our approach also leads to sharp integrability conditions for validity of the cumulant formula, as required by many of our examples, including iterated stochastic integrals, Lévy area, Bessel processes, KPZ with smooth noise, Wiener-Itô chaos and "rough" stochastic (forward) variance models.
