交织扩散过程与波动方程
Intertwining diffusions and wave equations
AI总结：
该研究建立任意维度交织扩散过程的一般理论，通过SDE构造交织关系并证明其对应双曲偏微分方程非负解，统一新旧案例，提出构造复杂交织的系统方法，还探讨了与对偶性等的关联。
摘要：
我们建立了任意维度下交织扩散过程的一般理论。核心结果给出了扩散过程交织关系的随机微分方程（SDE）构造，并证明其对应双曲型偏微分方程的非负解。例如，经典波动方程的解对应两个布朗运动的交织关系。该理论统一了诸多早期的交织案例（如β-γ代数的过程扩展）与近年案例（如二维生长模型研究中出现的交织）。我们还发现了多类新的交织关系，并提出通过组合简单交织构造更复杂交织的系统方法，其中“正交波”可将一维交织组合为多维交织。此外，本文还探讨了该理论与对偶性、时间反转及Doob的h-变换的关联。
英文摘要：
We develop a general theory of intertwined diffusion processes of any dimension. Our main result gives an SDE construction of intertwinings of diffusion processes and shows that they correspond to nonnegative solutions of hyperbolic partial differential equations. For example, solutions of the classical wave equation correspond to the intertwinings of two Brownian motions. The theory allows us to unify many older examples of intertwinings, such as the process extension of the beta-gamma algebra, with more recent examples such as the ones arising in the study of two-dimensional growth models. We also find many new classes of intertwinings and develop systematic procedures for building more complex intertwinings by combining simpler ones. In particular, `orthogonal waves' combine unidimensional intertwinings to produce multidimensional ones. Connections with duality, time reversals and Doob's h-transforms are also explored.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
