We prove Wasserstein distance bounds between the probability distributions of stochastic integrals with jumps, based on the integrands appearing in their stochastic integral representations. Our approach does not rely on the Stein equation or on the propagation of convexity property for Markovian semigroups, and makes use instead of forward-backward stochastic calculus arguments. This allows us to consider a large class of target distributions constructed using Brownian stochastic integrals and pure jump martingales, which can be specialized to infinitely divisible target distributions with finite Lévy measure and Gaussian components.

中文翻译：

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前后积分的Wasserstein距离估计

我们基于出现在其随机积分表示中的被积物，证明了具有跳跃的随机积分的概率分布之间的Wasserstein距离界限。我们的方法不依赖于Stein方程或马尔可夫半群的凸性传播，而是代替了前向-后向随机演算参数。这使我们可以考虑使用布朗随机积分和纯跳跃mar构造的一大类目标分布，这些目标分布可以专门用于具有有限Lévy度量和高斯分量的无限可分目标分布。