标题： 关于Lévy随机面积过程的有限维联合特征函数 显示英文标题

标题： On the Finite Dimensional Joint Characteristic Function of Lévy's Stochastic Area Processes

摘要： 本文的目标是推导耦合过程${(W_{t},L_{t}^{A}):t\in \lbrack 0,\infty)}$的有限维联合特征函数（有限维分布的傅里叶变换）的公式，其中$\{W_{t}:t\in \lbrack 0,\infty)}$是一个$d$维布朗运动，$\{L_{t}^{A}:t\in \lbrack 0,\infty)}$是与一个$d\times d$矩阵$A.$相关的广义$d$维 L$\acute{e}$莱维随机面积过程。这里$A$不必是对称的，在我们的计算中允许$A$变化。 问题最终归结为对称矩阵Riccati方程的递归系统的求解和一组独立的一阶线性矩阵ODE系统的求解。 作为示例，二维Lévy的随机面积过程被详细研究。 显示英文摘要

摘要： The goal of this paper is to derive a formula for the finite dimensional joint characteristic function (the Fourier transform of the finite dimensional distribution) of the coupled process ${(W_{t},L_{t}^{A}):t\in \lbrack 0,\infty)}$, where $\{W_{t}:t\in \lbrack 0,\infty)}$ is a $d$-dimensional Brownian motion and $\{L_{t}^{A}:t\in \lbrack 0,\infty)}$ is the generalized $d$-dimensional L$\acute{e}$vy's stochastic area process associated to a $d\times d$ matrix $A.$ Here $A$ need not be skew-symmetric, and in our computation we allow $A$ to vary. The problem finally reduces to the solution of a recursive system of symmetric matrix Riccati equations and a system of independent first order linear matrix ODEs. As an example, the two dimensional L\'{e}vy's stochastic area process is studied in detail.