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摘要翻译：
我们在概率空间中考虑过滤一致的非线性期望，只满足通常的条件和可分性。在控制假设下，我们证明了这些非线性期望可以表示为具有Lipschitz连续驱动项的倒向随机微分方程的解，其中鞅和驱动项都允许跳跃，且鞅表示为无穷维。为了建立这一结果，我们证明了这个控制条件足以保证BSDEs的比较定理成立，并将Peng的非线性Doob-Meyer分解推广到一般情况下。
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英文标题：
《Representing filtration consistent nonlinear expectations as
$g$-expectations in general probability spaces》
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作者：
Samuel N. Cohen
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最新提交年份：
2011
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分类信息：
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous drivers, where both the martingale and the driver terms are permitted to jump, and the martingale representation is infinite dimensional. To establish this result, we show that this domination condition is sufficient to guarantee that the comparison theorem for BSDEs will hold, and we generalise the nonlinear Doob-Meyer decomposition of Peng to a general context.
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PDF链接：
https://arxiv.org/pdf/1102.5287
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