## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

MCRF

In this paper, we develop a new approach to establish gradient estimates for positive solutions to the heat equation of elliptic or subelliptic operators on Euclidean spaces or on Riemannian manifolds.
More precisely, we give some estimates
of the gradient of logarithm of a positive solution via the uniform bound of
the logarithm of the solution. Moreover, we give a generalized version of
Li-Yau's estimate. Our proof is based on the link between PDE and quadratic
BSDE. Our method might be useful to study some (nonlinear) PDEs.

DCDS

In F. Delbaen, Y. Hu and A. Richou (Ann. Inst. Henri Poincaré Probab. Stat. 47(2):559--574, 2011), the authors proved that uniqueness of solution to quadratic BSDE with convex generator and unbounded terminal condition holds among solutions whose exponentials are $L^p$ with $p$ bigger than a constant $\gamma$ ($p>\gamma$).
In this paper, we consider the critical case: $p=\gamma$. We prove that the uniqueness holds among solutions whose exponentials are $L^\gamma$ under the additional assumption that the generator is
strongly convex. These exponential moments are natural as they are given by the existence theorem.

keywords:
unbounded terminal conditions
,
Quadratic BSDEs
,
convex generators
,
uniqueness.
,
critical case

DCDS

This paper is concerned with the switching game of a one-dimensional backward
stochastic differential equation (BSDE). The associated Bellman-Isaacs equation is a system of matrix-valued BSDEs living in a special unbounded convex domain with reflection on
the boundary along an oblique direction. In this paper, we show the existence of an adapted solution to this system of BSDEs with oblique reflection by the
penalization method, the monotone convergence, and the a priori estimates.

## Year of publication

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