5 citations · 5 across the 5 of their papers we have counts for
5 papers
Viscosity solutions to second order parabolic PDEs on Riemannian manifolds
Xuehong Zhu
In this work we consider viscosity solutions to second order parabolic PDEs defined on compact Riemannian manifolds with boundary conditions. We prove…
On the comparison theorem for multidimensional SDEs with jumps
Xuehong Zhu
In this note, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional stochastic differential equations (SDEs) with jumps and for…
Backward stochastic viability property with jumps and applications to the comparison theorem for multidimensional BSDEs with jumps
Xuehong Zhu
In this paper, we study conditions under which the solutions of a backward stochastic differential equation with jump remains in a given set of constrains. This property is the so-…
The viability property of jump diffusion processes on Riemannian manifolds
Xuehong Zhu
In this note, we consider the necessary and sufficient condition for viability property of diffusion processes with jumps on closed submanifolds of with some concrete examp…
The optimal control related to Riemannian manifolds and the viscosity solutions to H-J-B equations
Xuehong Zhu
This paper is concerned with the Dynamic Programming Principle (DPP in short) with SDEs on Riemannian manifolds. Moreover, through the DPP, we conclude that the cost function is th…