8 papers · 1 filter
The canonical SLE-reversible Weil--Petersson response diffusion
Chunhao Cai
The rough response calculus for the rotationally marked SLE welding law gives a closed Weil--Petersson energy but does not by itself give a process on rough weldings. For $0<κ\leq4…
Closed Response Calculus and Joint Densities for the Liouville Quantum Gravity Metric
Chunhao Cai
We give a general criterion for transferring first-order responses on an underlying probability space to a closed differential calculus on the law of an observable. An integration-…
Spectral Simplicity and Joint Eigenvalue Densities for a Non-Gaussian Brownian Time Change
Chunhao Cai
We study a Brownian time change on the unit square whose speed measure is constructed from a Dirichlet eigenfunction expansion with independent non-Gaussian coefficients. For $0<γ<…
Response Calculus for Spectral Simplicity and Joint Eigenvalue Densities
Chunhao Cai
We develop a perturbative response calculus for spectral problems obtained by changing the speed measure of a fixed symmetric energy form in a Gaussian environment. If Cameron--Mar…
Truncated Signature Information for Mixed Fractional Brownian Paths
Chunhao Cai
We study finite expected-signature information for mixed-fBm paths with Hurst indices above . Up to level three, the only parameter-dependent expected features are the varianc…
A mixed fractional CIR model: positivity and an implicit Euler scheme
Cong Zhang, Chunhao Cai
We consider a Cox--Ingersoll--Ross (CIR) type short rate model driven by a mixed fractional Brownian motion. Let be a one-dimensional mixed fractional Brownian motion wit…
LAN Property for the Drift and Hurst Paramters in The Mixed Fractional O-U Process with Continuous Observations
Chunhao Cai, Cong Zhang
This paper deals with the Local Asymptotical normality for the joint drift parameter and Hurst parameter in the mixed fractional Ornstein-Uhlenbeck process. Different from…
RNN-BSDE method for high-dimensional fractional backward stochastic differential equations with Wick-Itô integrals
Chunhao Cai, Cong Zhang
Fractional Brownian motions(fBMs) are not semimartingales so the classical theory of Itô integral can't apply to fBMs. Wick integration as one of the applications of Malliavin calc…