6 papers
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…
Re(Visiting) Time Series Foundation Models in Finance
Eghbal Rahimikia, Hao Ni, Weiguan Wang
Financial time series forecasting is central to trading, portfolio optimization, and risk management, yet it remains challenging due to noisy, non-stationary, and heterogeneous dat…
SPDEBench: An Extensive Benchmark for Learning Stochastic PDEs
Yuantu Zhu, Zheyan Li, Dai Shi +8
Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence…
High Rank Path Development: an approach of learning the filtration of stochastic processes
Jiajie Tao, Hao Ni, Chong Liu
Since the weak convergence for stochastic processes does not account for the growth of information over time which is represented by the underlying filtration, a slightly erroneous…
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…
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…