PreprintCC BY-NC-ND 4.0HAL
Backward doubly stochastic differential equations with or without reflection under weak conditions
Abstract
In this paper, we study the solvability of backward doubly stochastic differential equations (BDSDEs, for short), both with and without reflection, under weak conditions on the generator. First, when the generator f is of general growth in y and linear growth in z, we establish the existence, uniqueness, comparison principle, and the existence of maximal solutions. Second, when f is of linear growth in y and quadratic growth in z with bounded terminal value, we prove the existence, uniqueness, and comparison principle. Finally, when f is of general growth in y and quadratic growth in z with bounded terminal value, we prove the existence of maximal solutions.
Related
- Backward and reflected backward stochastic differential equations under initial enlargement of Brownian filtrations
- Backward stochastic partial differential equations with unbounded random coefficients
- Conditional Reflected Backward Stochastic Differential Equations
- Multidimensional Infinite-Horizon Markovian Backward Stochastic Differential Equations with Continuous Coefficients and Nonzero-Sum Differential Games
- Rough backward stochastic differential equations
BibTeX
@misc{gao2026backward,
title = {{Backward doubly stochastic differential equations with or without reflection under weak conditions}},
author = {Shuxian Gao and Ying Hu and Jiaqiang Wen},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2603.14447},
eprint = {2603.14447},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05751212v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Backward doubly stochastic differential equations with or without reflection under weak conditions
AU - Shuxian Gao
AU - Ying Hu
AU - Jiaqiang Wen
PY - 2026
DA - 2026/09/15
PB - HAL
DO - 10.48550/arxiv.2603.14447
UR - https://hal.science/hal-05751212v1
AB - In this paper, we study the solvability of backward doubly stochastic differential equations (BDSDEs, for short), both with and without reflection, under weak conditions on the generator. First, when the generator f is of general growth in y and linear growth in z, we establish the existence, uniqueness, comparison principle, and the existence of maximal solutions. Second, when f is of linear growth in y and quadratic growth in z with bounded terminal value, we prove the existence, uniqueness, and comparison principle. Finally, when f is of general growth in y and quadratic growth in z with bounded terminal value, we prove the existence of maximal solutions.
ER -