Strong solutions of SDES with singular drift and Sobolev diffusion coefficients

By Xicheng Zhang. 2005

163 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/de728b8bdd19803f88b3e02c392a2eba9f905edd

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Pathwise uniqueness for singular SDEs driven by stable processes (2010, result): “This result has been generali z d in various directions in [9], [13], [27], [6], [7], [5], [8].”
Gradient estimates and applications for SDEs in Hilbert space with multiplicative noise and Dini continuous drift (2014, background): “We would also like to mention that for SDEs on R with a nice non-degenerate multiplicative noise, the existence and uniqueness of solutions have been proved in [26] if the drift is in L 2(d+1) loc ([0,∞)× R).”
Stochastic flows of SDEs with irregular coefficients and stochastic transport equations (2009, background): “On the other hand, whenσ is non-degenerate andb is not continuous and even singular, SDE (1.1) may have a unique strong solution for each starting point x ∈ Rd (cf. [14, 17, 26], etc.).”
Hölder Flow and Differentiability for SDEs with Nonregular Drift (2013, background): “, [2]), where the case of a diffusion coefficient different from the identity is studied, with slightly stronger assumptions on b, and following works.”
Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients (2014, background): “MR3010120 SCHOOL OF MATHEMATICS AND STATISTICS WUHAN UNIVERSITY WUHAN, HUBEI 430072 P.R. CHINA E-MAIL: xlj.98@whu.edu.cn XichengZhang@gmail.com”
Ergodicity of stochastic differential equations with jumps and singular coefficients (2017, background): “Latter, the second named author [51, 52] extended their result to the multiplicative noise case under some non-degenerate and Sobolev conditions on the diffusion coefficient.”
Flow of diffeomorphisms for SDEs with unbounded H (2009, background): “More recent papers dealing with such approach are [12,16,30,32] (see also the references therein).”
Stochastic differential equations with Sobolev diffusion and singular drift and applications (2016, background): “Moreover, unlike [28] and [30], there is no explosion time problem here since we are assuming global integrability conditions on σ and b; see Lemma 6.”
Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients (2010, background): “In the case of non-constant and non-degenerate di ffusion coefficient, the present author [15] proved the pathwise uniqueness for SDE (1.”