L 1 and L ∞ stability of transition densities of perturbed diffusions

IF 0.3 Q4 STATISTICS & PROBABILITY Random Operators and Stochastic Equations Pub Date : 2021-11-20 DOI:10.1515/rose-2021-2067
I. Bitter, V. Konakov
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引用次数: 1

Abstract

Abstract In this paper, we derive a stability result for L 1 {L_{1}} and L ∞ {L_{\infty}} perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth, and the estimates reflect the transport of the initial condition by the unbounded drift through the corresponding flow. Our approach is based on the study of the distance in L 1 {L_{1}} - L 1 {L_{1}} metric between the transition densities of a given diffusion and the perturbed one using the McKean–Singer parametrix expansion. In the second part, we generalize the well-known result on the stability of diffusions with bounded coefficients to the case of at most linearly growing drift.
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扰动扩散跃迁密度的L1和L∞稳定性
摘要本文给出了扩散的L1{L_{1}}和L∞{L_{{infty}扰动在弱正则性条件下的稳定性结果。特别是,我们考虑的漂移项最多可以是线性增长的无界漂移项,并且估计反映了无界漂移通过相应流对初始条件的传输。我们的方法是基于使用McKean–Singer参数展开来研究给定扩散的跃迁密度和扰动扩散的跃迁浓度之间在L1{L_{1}}-L1{L_{1}}度量中的距离。在第二部分中,我们将关于有界系数扩散稳定性的众所周知的结果推广到漂移至多线性增长的情况。
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来源期刊
Random Operators and Stochastic Equations
Random Operators and Stochastic Equations STATISTICS & PROBABILITY-
CiteScore
0.60
自引率
25.00%
发文量
24
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