Multidimensional singular Stochastic differential equations

Xicheng Zhang

doi:10.1007/978-3-319-74929-7_26

Multidimensional singular Stochastic differential equations

Xicheng Zhang^*

^*Corresponding author for this work

Wuhan University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

In this paper we survey recent progress about multidimensional stochastic differential equations with singular drifts and Sobolev diffusion coefficients. Moreover, applications to Navier–Stokes equations and SPDEs are also presented.

Original language	English
Title of host publication	Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016
Editors	Gerald Trutnau, Andreas Eberle, Walter Hoh, Moritz Kassmann, Martin Grothaus, Wilhelm Stannat
Publisher	Springer New York LLC
Pages	391-403
Number of pages	13
ISBN (Print)	9783319749280
DOIs	https://doi.org/10.1007/978-3-319-74929-7_26
Publication status	Published - 2018
Externally published	Yes
Event	International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016 - Bielefeld, Germany Duration: 10 Oct 2016 → 14 Oct 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	229
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016
Country/Territory	Germany
City	Bielefeld
Period	10/10/16 → 14/10/16

Keywords

Krylov’s estimate
Stochastic flow
Zvonkin’s transformation

Access to Document

10.1007/978-3-319-74929-7_26

Cite this

Zhang, X. (2018). Multidimensional singular Stochastic differential equations. In G. Trutnau, A. Eberle, W. Hoh, M. Kassmann, M. Grothaus, & W. Stannat (Eds.), Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016 (pp. 391-403). (Springer Proceedings in Mathematics and Statistics; Vol. 229). Springer New York LLC. https://doi.org/10.1007/978-3-319-74929-7_26

Zhang, Xicheng. / Multidimensional singular Stochastic differential equations. Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. editor / Gerald Trutnau ; Andreas Eberle ; Walter Hoh ; Moritz Kassmann ; Martin Grothaus ; Wilhelm Stannat. Springer New York LLC, 2018. pp. 391-403 (Springer Proceedings in Mathematics and Statistics).

@inproceedings{3a17efae15d44ea98c278fece1124ca8,

title = "Multidimensional singular Stochastic differential equations",

abstract = "In this paper we survey recent progress about multidimensional stochastic differential equations with singular drifts and Sobolev diffusion coefficients. Moreover, applications to Navier–Stokes equations and SPDEs are also presented.",

keywords = "Krylov{\textquoteright}s estimate, Stochastic flow, Zvonkin{\textquoteright}s transformation",

author = "Xicheng Zhang",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016 ; Conference date: 10-10-2016 Through 14-10-2016",

year = "2018",

doi = "10.1007/978-3-319-74929-7_26",

language = "English",

isbn = "9783319749280",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "391--403",

editor = "Gerald Trutnau and Andreas Eberle and Walter Hoh and Moritz Kassmann and Martin Grothaus and Wilhelm Stannat",

booktitle = "Stochastic Partial Differential Equations and Related Fields - In Honor of Michael R{\"o}ckner SPDERF, 2016",

}

Zhang, X 2018, Multidimensional singular Stochastic differential equations. in G Trutnau, A Eberle, W Hoh, M Kassmann, M Grothaus & W Stannat (eds), Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. Springer Proceedings in Mathematics and Statistics, vol. 229, Springer New York LLC, pp. 391-403, International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016, Bielefeld, Germany, 10/10/16. https://doi.org/10.1007/978-3-319-74929-7_26

Multidimensional singular Stochastic differential equations. / Zhang, Xicheng.
Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. ed. / Gerald Trutnau; Andreas Eberle; Walter Hoh; Moritz Kassmann; Martin Grothaus; Wilhelm Stannat. Springer New York LLC, 2018. p. 391-403 (Springer Proceedings in Mathematics and Statistics; Vol. 229).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Multidimensional singular Stochastic differential equations

AU - Zhang, Xicheng

N1 - Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - In this paper we survey recent progress about multidimensional stochastic differential equations with singular drifts and Sobolev diffusion coefficients. Moreover, applications to Navier–Stokes equations and SPDEs are also presented.

AB - In this paper we survey recent progress about multidimensional stochastic differential equations with singular drifts and Sobolev diffusion coefficients. Moreover, applications to Navier–Stokes equations and SPDEs are also presented.

KW - Krylov’s estimate

KW - Stochastic flow

KW - Zvonkin’s transformation

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U2 - 10.1007/978-3-319-74929-7_26

DO - 10.1007/978-3-319-74929-7_26

M3 - Conference contribution

AN - SCOPUS:85050005566

SN - 9783319749280

T3 - Springer Proceedings in Mathematics and Statistics

SP - 391

EP - 403

BT - Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016

A2 - Trutnau, Gerald

A2 - Eberle, Andreas

A2 - Hoh, Walter

A2 - Kassmann, Moritz

A2 - Grothaus, Martin

A2 - Stannat, Wilhelm

PB - Springer New York LLC

T2 - International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016

Y2 - 10 October 2016 through 14 October 2016

ER -

Zhang X. Multidimensional singular Stochastic differential equations. In Trutnau G, Eberle A, Hoh W, Kassmann M, Grothaus M, Stannat W, editors, Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. Springer New York LLC. 2018. p. 391-403. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-319-74929-7_26

Multidimensional singular Stochastic differential equations

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