arXiv subjects

Mengbo Zhu

Publications and source records attributed to Mengbo Zhu.

4 recordsLinked to original sources

arXiv2026

A note on convergence rate for reflected BSDEs with quadratic generators by penalization method

In this paper, we study the convergence rate between reflected backward stochastic differential equations with quadratic generators and their penalized BSDEs. Using techniques of BMO martingales, we prove the convergence rate is at order $\frac{1}{2}$ as a function of the penalty parameter. Finally, the result is applied to study numerical approximation of reflected BSDEs with sub-quadratic generators by the Euler's polygonal line method.

math.PR↗

arXiv2026

Doubly Reflected Backward SDEs Driven by $G$-Brownian Motion with Quadratic Generator

In this paper, we study the doubly reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs for short) when the generator has quadratic growth in the $z$-component. Based on the theory of $G$-BMO martingale and $G$-Girsanov theorem, we establish the existence and uniqueness result when the upper obstacle is almost a generalized $G$-Itô's process. Moreover, the solution can be approximated monotonically by the solutions to a family of penalized reflected $G$-BSDEs with a lower obstacle, which plays an important role to establish the relation between doubly reflected $G$-BSDEs and fully nonlinear partial differential equations with double obstacles.

math.PR↗

arXiv2023

Computational Study of Rarefied Gas Flow and Heat Transfer in Lid-driven Cylindrical Cavities

The gas flow characteristics in lid-driven cavities are influenced by several factors, such as cavity geometry, gas properties, and boundary conditions. In this study, the physics of heat and gas flow in cylindrical lid-driven cavities with various cross-sections, including fully or partially rounded edges, is investigated through numerical simulations using the direct simulation Monte Carlo (DSMC) and the discrete unified gas kinetic scheme (DUGKS) methods. The thermal and fluid flow fields are systematically studied for both constant and oscillatory lid velocities, for various degrees of gas rarefaction ranging from the slip to the free-molecular regimes. The impact of expansion cooling and viscous dissipation on the thermal and flow fields, as well as the occurrence of counter-gradient heat transfer (also known as anti-Fourier heat transfer) under non-equilibrium conditions, are explained based on the results obtained from numerical simulations. Furthermore, the influence of the incomplete tangential accommodation coefficient on the thermal and fluid flow fields is discussed. A comparison is made between the thermal and fluid flow fields predicted in cylindrical cavities and those in square-shaped cavities. The present work contributes to the advancement of micro/nano-electromechanical systems (MEMS/NEMS) by providing valuable insights into rarefied gas flow and heat transfer in lid-driven cavities.

physics.flu-dyn↗

arXiv2021

Diagonally quadratic BSDE with oblique reflection and optimal switching

The present paper is devoted to the study of diagonally quadratic backward stochastic differential equation with oblique reflection. Using a penalization approach, we show the existence fo a solution by providing some delicated a priori estimates. We further obtain the uniqueness by verifying the first component of the solution is indeed the value of a switching probelm for quadratic BSDEs. Moreover, we provide an extension for the solvability and apply our results to study a risk-sensitive switching problem for functional stochastic differential equations.

math.PR↗