6 citations · 26 across the 15 of their papers we have counts for
5 papers · 1 filter
On a maximal inequality and its application to SDEs with singular drift
Xuan Liu, Guangyu Xi
In this paper we present a Doob type maximal inequality for stochastic processes satisfying the conditional increment control condition. If we assume, in addition, that the margins…
A stochastic Pontryagin maximum principle on the Sierpinski gasket
Xuan Liu
In this paper, we consider stochastic control problems on the Sierpinski gasket. An order comparison lemma is derived using heat kernel estimate for Brownian motion on the gasket.…
Backward problems for stochastic differential equations on the Sierpinski gasket
Xuan Liu, Zhongmin Qian
In this paper, we study the non-linear backward problems (with deterministic or stochastic durations) of stochastic differential equations on the Sierpinski gasket. We prove the ex…
On the maximum of a type of random processes
Xuan Liu
We consider a type of random processes which satisfies the conditional increment condition and obtain an estimate for the tail probability and a Doob-type inequality of the maximum…
A Quasi-sure Non-degeneracy Property for the Brownian Rough Path
Horatio Boedihardjo, Xi Geng, Xuan Liu +1
In the present paper, we are going to show that outside a slim set in the sense of Malliavin (or quasi-surely), the signature path (which consists of iterated path integrals in eve…