arXiv subjects

Yuejuan Xi

Publications and source records attributed to Yuejuan Xi.

4 recordsLinked to original sources

arXiv2020

Parameter estimation for threshold Ornstein-Uhlenbeck processes from discrete observations

Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we need to find the explicit form of the invariant measure. With the sampling time step arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sample size tends to infinity.

math.ST↗

arXiv2020

The first passage time on the (reflected) Brownian motion with broken drift hitting a random boundary

In this paper we consider a (reflected) Brownian motion with broken drift hitting a random boundary. Some dedicated calculations allow us to obtain the formula on the joint Laplace transform of the hitting time and hitting position. These develop the research on first rendezvous times of (reflected) Brownian motion and compound Poisson-type processes by Perry et al. (2004).

math.PR↗

arXiv2020

Estimation of all parameters in the reflected Orntein-Uhlenbeck process from discrete observations

Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling time step h > 0 arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sampling size n tends to infinity. This provides a complete solution to an open problem left in Hu et al. [5].

math.ST↗

arXiv2020

Local time of infinite time horizon Brownian bridge

We introduce an infinite time horizon Brownian bridge which is determined by a stochastic Langevin equation with time dependent drift coefficient. We show that this process goes to zero almost surely when the time goes to infinity and study the existence and asymptotic behavior of its local time as well as its Hölder continuity in time variable and in location variable. The main difficulty is the lack of stationarity of the process so that the powerful tools for stationary (Gaussian) processes are not applicable. We employ the Garsia-Rodemich-Rumsey inequality to get around this type of difficulty.

math.PR↗