发表机构
Institute of Mathematics, University of Gießen（吉森大学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究对称正半定矩阵锥上的仿射随机Volterra方程，建立弱存在性并推导Fourier-Laplace变换公式，进而扩展Gibson-Schwartz商品模型为Volterra-Wishart过程，使方差具有记忆性和随机瞬时相关性，同时保持仿射可处理性。
AI 中文摘要
我们在对称正半定矩阵锥上研究仿射随机Volterra方程。对于作用于矩阵动态的逐项标量核，我们利用凸域上Volterra方程的随机不变性结果建立弱存在性，并推导出由矩阵值Riccati-Volterra方程刻画的条件Fourier-Laplace变换公式。作为应用，我们通过用Volterra-Wishart过程替换其方差-协方差结构来扩展Gibson-Schwartz商品模型。所得模型允许方差具有记忆性以及随机瞬时相关性，同时保持仿射可处理性。其联合Fourier-Laplace变换具有由矩阵Riccati-Volterra方程控制的指数仿射表示。虽然本文考虑的存在性理论排除了在原点处奇异的核，但平移分数核仍然允许，并提供具有幂律记忆的可处理规范。
英文摘要
We study affine stochastic Volterra equations on the cone of symmetric positive semidefinite matrices. For scalar kernels acting entrywise on the matrix dynamics, we establish weak existence by exploiting stochastic invariance results for Volterra equations on convex domains and derive a conditional Fourier--Laplace transform formula characterized by matrix-valued Riccati--Volterra equations. As an application, we extend the Gibson--Schwartz commodity model by replacing its variance-covariance structure with a Volterra--Wishart process. The resulting model allows for memory in the variances and for stochastic instantaneous correlation, while retaining affine tractability. Its joint Fourier--Laplace transform admits an exponential-affine representation governed by a matrix Riccati--Volterra equation. While the existence theory considered here excludes kernels that are singular at the origin, shifted fractional kernels remain admissible and provide a tractable specification with power-law memory.
