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math.PR2026
The -bounds for Derivatives of Unitary Developments of Random Continuous Geometric Rough Paths
Chong Liu, Zijiu Lyu, Hao Ni
In this paper we derive an explicit formula for derivatives of unitary developments of random continuous geometric rough paths of all orders and establish proper -bounds for t…
math.PR2024
Restricted Path Characteristic Function Determines the Law of Stochastic Processes
Siran Li, Zijiu Lyu, Hao Ni +1
A central question in rough path theory is characterising the law of stochastic processes on path spaces. It is established in [I. Chevyrev & T. Lyons, Characteristic functions of…
math.PR2024
A PDE approach for solving the characteristic function of the generalised signature process
Terry Lyons, Hao Ni, Jiajie Tao
The signature of a path, as a fundamental object in Rough path theory, serves as a generating function for non-commutative monomials on path space. It transforms the path into a gr…