Strong Solutions of Stochastic Differential Equations with Coefficients in Mixed-Norm Spaces

Ling, Chengcheng; Xie, Longjie

doi:10.1007/s11118-021-09913-4

Cited by 11 publications

(8 citation statements)

References 19 publications

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“…In this part, we collect the known results on regularity estimates for corresponding PDEs. [25, Theorem 3.2] and [16,Theorem 2.1] show that the Kolmogorov backward equation corresponding to the solution to SDE (1.1) can be solved in L q p (T ) under the following assumption.…”

Section: A Auxiliary Results On Kolmogorov Backward Equationsmentioning

confidence: 99%

A Wong-Zakai theorem for SDEs with singular drift

Ling¹,

Riedel²,

Scheutzow³

2021

Preprint

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We study stochastic differential equations (SDEs) with multiplicative Stratonovich-type noise of the formwith a possibly singular drift b ∈ L p (R d ), p > d and p 2, and show that such SDEs can be approximated by random ordinary differential equations by smoothing the noise and the singular drift at the same time. We further prove a support theorem for this class of SDEs in a rather simple way using the Girsanov theorem.

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Section: A Auxiliary Results On Kolmogorov Backward Equationsmentioning

confidence: 99%

A Wong-Zakai theorem for SDEs with singular drift

Ling¹,

Riedel²,

Scheutzow³

2021

Preprint

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“…So our first task is to extend [25,49] to the case of mixed L p -spaces. We must mention that although Ling and Xie [29] has already considered the singular SDEs in mixed L p -spaces, their result can not be applied to the above equation due to the new feature that we need to consider the order of integrability in x, y as well as the different integrability indices. Note that in [37], the last two authors of the present paper have already shown the weak and strong well-posedness for DDSDE (1.2) when b(t, x, µ) = R d φ t (x, y)µ(dy) (see also [28] and [34] for bounded measurable interaction kernel φ).…”

Section: Introductionmentioning

confidence: 99%

Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions

Hao¹,

Röckner²,

Zhang³

2022

Preprint

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In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular L p -interactions as well as the moderate interaction particle system in the level of particle trajectories. One of the main obstacles is to establish the strong well-posedness of particle system with singular interaction. In particular, we develop the theory of strong well-posedness of Krylov and Röckner [25] in the case of mixed L p -drifts, where the heat kernel estimates play a crucial role. Moreover, when the interaction kernel is bounded measurable, we also obtain the optimal rate of strong convergence, which is partially based on Jabin and Wang's entropy method [19] and Zvonkin's transformation.

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“…The stochastic Gronwall inequality without supremum is applied to study various SDEs without memory, see e.g. [9], [13], [14], [17], [20], [25], [29], [30], [33], [35] and [37].…”

Section: Introductionmentioning

confidence: 99%

Concave and other generalizations of stochastic Gronwall inequalities

Geiss¹

2022

Preprint

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We provide nonlinear generalizations of a class of stochastic Gronwall inequalities that have been studied by von Renesse and Scheutzow (2010), Scheutzow (2013), Xie and Zhang (2020) and Mehri and Scheutzow (2021). This class of stochastic Gronwall inequalities is a useful tool for SDEs.More precisely, we study generalizations of the Bihari-LaSalle type. Whilst in a closely connected article by the author convex generalizations are studied, we investigate here concave and other generalizations. These types of estimates are useful to obtain existence and uniqueness of global solutions of path-dependent SDEs driven by Lévy processes under one-sided non-Lipschitz monotonicity and coercivity assumptions.

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Strong Solutions of Stochastic Differential Equations with Coefficients in Mixed-Norm Spaces

Cited by 11 publications

References 19 publications

A Wong-Zakai theorem for SDEs with singular drift

A Wong-Zakai theorem for SDEs with singular drift

Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions

Concave and other generalizations of stochastic Gronwall inequalities

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