2017/12/19 by Yi Shen, Shen, Yi, Yizao Wang +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1712.07082
openalex publication_date 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose an aggregated random-field model, and investigate the scaling limits of the aggregated partial-sum random fields. In our model, each copy of the random field in the aggregation is built from two correlated one-dimensional random walks, each with a random persistence parameter. When the persistence parameters are independent, the scaling limit is a fractional Brownian sheet. When the persistence parameters are dependent, the scaling limit is more delicate, and in particular depends on the growth rates of the underlying rectangular region along two directions: at different rates different operator-scaling Gaussian random fields appear as the region area tends to infinity. In particular, at the so-called critical speed, a large family of Gaussian random fields with long-range dependence arise in the limit. We also identify four different regimes at non-critical speed where fractional Brownian sheets arise in the limit.