论文标题
非共同随机演算中的准剃须代数
Quasi-shuffle algebras in non-commutative stochastic calculus
论文作者
论文摘要
本章分为两个部分。第一个主要是说明性的，并建立在Karandikar对矩阵值的半明星 - 粒子 - 微分钟的{}演算的基础上。它的目的是详细展开对迭代{}和Stratonovich积分所暗示的代数结构。这些构造概括了陈计算的经典规则，以确定性标量迭代的迭代积分。第二部分在控制理论中发展了通常称为年代积分的随机类似物。我们尤其获得了iT {progaured semimartingales的随机指数的对数的pre lie magnus公式。
This chapter is divided into two parts. The first is largely expository and builds on Karandikar's axiomatisation of It{ô} calculus for matrix-valued semimartin-gales. Its aim is to unfold in detail the algebraic structures implied for iterated It{ô} and Stratonovich integrals. These constructions generalise the classical rules of Chen calculus for deterministic scalar-valued iterated integrals. The second part develops the stochastic analog of what is commonly called chronological calculus in control theory. We obtain in particular a pre-Lie Magnus formula for the logarithm of the It{ô} stochastic exponential of matrix-valued semimartingales.
