Along the ideas of Curtain and Glover (in: Bart, Gohberg, Kaashoek (eds) Operator theory and systems, Birkhäuser, Boston, 1986), we extend the balanced truncation method for (infinite-dimensional) linear systems to arbitrary-dimensional bilinear and stochastic systems. In particular, we apply Hilbert space techniques used in many-body quantum mechanics to establish new fully explicit error bounds for the truncated system and prove convergence results. The functional analytic setting allows us to obtain mixed Hardy space error bounds for both finite-and infinite-dimensional systems, and it is then applied to the model reduction of stochastic evolution equations driven by Wiener noise.

遵循Curtain和Glover（在Bart，Gohberg，Kaashoek（eds）算子理论和系统中，Birkhäuser，Boston，1986年）的思想，我们将（无限维）线性系统的平衡截断方法扩展到任意维双线性和随机系统。特别地，我们应用多体量子力学中使用的希尔伯特空间技术为截断系统建立新的完全明确的误差界，并证明收敛结果。函数解析设置允许我们获得有限维和无限维系统的混合Hardy空间误差界，然后将其应用于由Wiener噪声驱动的随机演化方程的模型简化。