6 papers
First-Order Convergence of Monotone Schemes for Hamilton--Jacobi Equations on the Wasserstein Space on Graphs
Jianbo Cui, Tonghe Dang
We prove first-order convergence of semi-discrete monotone finite difference schemes for Hamilton--Jacobi equations on the Wasserstein space over a finite graph. A central challeng…
Quantifying the effect of graph structure on strong Feller property of SPDEs
Jianbo Cui, Tonghe Dang, Jialin Hong +1
This paper investigates how the structure of the underlying graph influences the behavior of stochastic partial differential equations (SPDEs) on finite tree graphs, where each edg…
Hamilton--Jacobi--Bellman equation for optimal control of stochastic Wasserstein--Hamiltonian system on graphs
Jianbo Cui, Tonghe Dang
Stochastic optimal control problems for Hamiltonian dynamics on graphs have wide-ranging applications in mechanics and quantum field theory, particularly in systems with graph-base…
Finite difference schemes for Hamilton--Jacobi equation on Wasserstein space on graphs
Jianbo Cui, Tonghe Dang, Chenchen Mou
This work proposes and studies numerical schemes for initial value problems of Hamilton--Jacobi equations (HJEs) with a graph individual noise on the Wasserstein space on graphs. N…
-strong convergence orders of fully discrete schemes for the SPDE driven by Lévy noise
Chuchu Chen, Tonghe Dang, Jialin Hong +1
It is well known that for a stochastic differential equation driven by Lévy noise, the temporal Hölder continuity in sense of the exact solution does not exceed . This…
A new class of splitting methods that preserve ergodicity and exponential integrability for stochastic Langevin equation
Chuchu Chen, Tonghe Dang, Jialin Hong +1
In this paper, we propose a new class of splitting methods to solve the stochastic Langevin equation, which can simultaneously preserve the ergodicity and exponential integrability…