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1

Solving high-dimensional partial differential equations using deep learning

Han, Jiequn, Jentzen, Arnulf, E, Weinan

Journal:

Proceedings of the National Academy of Sciences

Year:

2018

Language:

english

File:

PDF, 878 KB

english, 2018

2

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

E, Weinan, Han, Jiequn, Jentzen, Arnulf

Journal:

Communications in Mathematics and Statistics

Year:

2017

Language:

english

File:

PDF, 1.20 MB

english, 2017

3

Digital Speed Control of a DC Motor With Phase-Locked Loop Regulation

Bose, Bimal K., Jentzen, Kenneth J.

Journal:

IEEE Transactions on Industrial Electronics and Control Instrumentation

Year:

1978

Language:

english

File:

PDF, 2.31 MB

english, 1978

4

Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients

Conus, Daniel, Jentzen, Arnulf, Kurniawan, Ryan

Journal:

The Annals of Applied Probability

Year:

2019

Language:

english

File:

PDF, 599 KB

english, 2019

5

The Numerical Approximation of Stochastic Partial Differential Equations

A. Jentzen, P. E. Kloeden

Journal:

Milan Journal of Mathematics

Year:

2009

Language:

english

File:

PDF, 439 KB

english, 2009

6

Overcoming the Order Barrier in the Numerical Approximation of Stochastic Partial Differential Equations with Additive Space-Time Noise

Arnulf Jentzen and Peter E. Kloeden

Journal:

Proceedings Mathematical Physical & Engineering Sciences

Year:

2009

Language:

english

File:

PDF, 1.16 MB

english, 2009

7

Destructive Hostility

Jentzen, Jeffrey, Palermo, George, Johnson, L. Thomas, Khang-Cheng, H o, Stormo, K. Alan, Teggatz, John

Journal:

American Journal of Forensic Medicine & Pathology

Year:

1994

File:

PDF, 772 KB

1994

8

Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations

Hutzenthaler, Martin, Jentzen, Arnulf, Kloeden, Peter E.

Journal:

The Annals of Applied Probability

Year:

2013

Language:

english

File:

PDF, 594 KB

english, 2013

9

Strong convergence for explicit space–time discrete numerical approximation methods for stochastic Burgers equations

Jentzen, Arnulf, Salimova, Diyora, Welti, Timo

Journal:

Journal of Mathematical Analysis and Applications

Year:

2019

Language:

english

File:

PDF, 725 KB

english, 2019

10

Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients

A. Jentzen, P. E. Kloeden, A. Neuenkirch

Journal:

Numerische Mathematik

Year:

2009

Language:

english

File:

PDF, 378 KB

english, 2009

11

Neck and Scleral Hemorrhage in Drowning

Russell T. Alexander, Jeffrey M. Jentzen

Journal:

Journal of Forensic Sciences

Year:

2011

Language:

english

File:

PDF, 258 KB

english, 2011

12

Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise

Arnulf Jentzen, Michael Röckner

Journal:

Journal of Differential Equations

Year:

2012

Language:

english

File:

PDF, 286 KB

english, 2012

13

Taylor Approximations for Stochastic Partial Differential Equations || 5. Stochastic Partial Differential Equations

Jentzen, Arnulf, Kloeden, Peter E.

Year:

2011

Language:

english

File:

PDF, 167 KB

english, 2011

14

TAYLOR EXPANSIONS OF SOLUTIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE

Arnulf Jentzen and Peter Kloeden

Journal:

The Annals of Probability

Year:

2010

Language:

english

File:

PDF, 1.85 MB

english, 2010

15

Taylor Approximations for Stochastic Partial Differential Equations || 8. Taylor Approximations for SPDEs with Multiplicative Noise

Jentzen, Arnulf, Kloeden, Peter E.

Year:

2011

Language:

english

File:

PDF, 335 KB

english, 2011

16

Taylor Approximations for Stochastic Partial Differential Equations || 6. Numerical Methods for SPDEs

Jentzen, Arnulf, Kloeden, Peter E.

Year:

2011

Language:

english

File:

PDF, 123 KB

english, 2011

17

Quantitative performance evaluation of 124I PET/MRI lesion dosimetry in differentiated thyroid cancer

Wierts, Roel, Jentzen, Walter, Quick, Harald H, Wisselink, Hendrik J, Pooters, Ivo N A, Wildberger, Joachim E, Herrmann, Ken, Kemerink, Gerrit J, Backes, Walter H, Mottaghy, Felix M

Journal:

Physics in Medicine and Biology

Year:

2017

Language:

english

File:

PDF, 1.37 MB

english, 2017

18

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

Beck, Christian, E, Weinan, Jentzen, Arnulf

Journal:

Journal of Nonlinear Science

Year:

2019

Language:

english

File:

PDF, 2.20 MB

english, 2019

19

Untersuchungen zum Bewegungsablauf motorisierter Knieschienen

B. Stünitz, W. Blauth, B. Jentzen

Journal:

European Journal of Trauma and Emergency Surgery

Year:

1993

File:

PDF, 1.10 MB

1993

20

Clinical applications of124I-PET/CT in patients with differentiated thyroid cancer

Lutz S. Freudenberg, Walter Jentzen, Alexander Stahl, Andreas Bockisch, Sandra J. Rosenbaum-Krumme

Journal:

European Journal of Nuclear Medicine and Molecular Imaging

Year:

2011

Language:

english

File:

PDF, 255 KB

english, 2011

21

Pathwise Taylor schemes for random ordinary differential equations

Arnulf Jentzen, Peter E. Kloeden

Journal:

BIT Numerical Mathematics

Year:

2009

Language:

english

File:

PDF, 557 KB

english, 2009

22

Death after discharge from the emergency department

Michael P Kefer, Stephen W Hargarten, Jeffrey Jentzen

Journal:

Annals of Emergency Medicine

Year:

1994

Language:

english

File:

PDF, 429 KB

english, 1994

23

Cocaine-induced myocarditis

Jeffrey m. Jentzen

Journal:

American Heart Journal

Year:

1989

Language:

english

File:

PDF, 150 KB

english, 1989

24

Arm Training Induced Brain Plasticity in Stroke Studied with Serial Positron Emission Tomography

G. Nelles, W. Jentzen, M. Jueptner, S. Müller, H.C. Diener

Journal:

Year:

2001

Language:

english

File:

PDF, 1.59 MB

english, 2001

25

Pathwise convergent higher order numerical schemes for random ordinary differential equations

Kloeden, Peter E., Jentzen, Arnulf

Journal:

Proceedings Mathematical Physical & Engineering Sciences

Year:

2007

Language:

english

File:

PDF, 333 KB

english, 2007

26

Galerkin Approximations for the Stochastic Burgers Equation

Blömker, Dirk, Jentzen, Arnulf

Journal:

SIAM Journal on Numerical Analysis

Year:

2013

Language:

english

File:

PDF, 298 KB

english, 2013

27

Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients

Hutzenthaler, M., Jentzen, A., Kloeden, P. E.

Journal:

Proceedings Mathematical Physical & Engineering Sciences

Year:

2011

Language:

english

File:

PDF, 210 KB

english, 2011

28

An Improved Maximum Allowable Transfer Interval for $L^{p}$-Stability of Networked Control Systems

Jentzen, A., Leber, F., Schneisgen, D., Berger, A., Siegmund, S.

Journal:

IEEE Transactions on Automatic Control

Year:

2010

Language:

english

File:

PDF, 324 KB

english, 2010

29

EFFICIENT SIMULATION OF NONLINEAR PARABOLIC SPDES WITH ADDITIVE NOISE

Arnulf Jentzen, Peter Kloeden and Georg Winkel

Journal:

The Annals of Applied Probability

Year:

2011

Language:

english

File:

PDF, 1.86 MB

english, 2011

30

Pathwise Convergent Higher Order Numerical Schemes for Random Ordinary Differential Equations

Peter E. Kloeden and Arnulf Jentzen

Journal:

Proceedings Mathematical Physical & Engineering Sciences

Year:

2007

Language:

english

File:

PDF, 1.05 MB

english, 2007

31

A Milstein Scheme for SPDEs

Jentzen, Arnulf, Röckner, Michael

Journal:

Foundations of Computational Mathematics

Year:

2015

Language:

english

File:

PDF, 1008 KB

english, 2015

32

Acute Zolpidem Overdose--Report of Two Cases

Gock, S. B., Wong, S. H. Y., Nuwayhid, N., Venuti, S. E., Kelley, P. D., Teggatz, J. R., Jentzen, J. M.

Journal:

Journal of Analytical Toxicology

Year:

1999

Language:

english

File:

PDF, 448 KB

english, 1999

33

Self-Intoxication with Morphine Obtained from an Infusion Pump

Gock, S. B., Wong, S. H., Stormo, K. A., Jentzen, J. M.

Journal:

Journal of Analytical Toxicology

Year:

1999

Language:

english

File:

PDF, 382 KB

english, 1999

34

Liquide, zukunftsund investitionsfähig sein

Journal:

Year:

2014

Language:

german

File:

PDF, 353 KB

german, 2014

35

Kein Zwiespalt – Therapeut und Unternehmer

Journal:

Year:

2014

Language:

german

File:

PDF, 595 KB

german, 2014

36

Position Paper on Fatal Abusive Head Injuries in Infants and Young Children

Case, Mary E., Graham, Michael A., Handy, Tracey Corey, Jentzen, Jeffrey M., Monteleone, James A.

Journal:

American Journal of Forensic Medicine & Pathology

Year:

2001

Language:

english

File:

PDF, 574 KB

english, 2001

37

Fentanyl-related Toxicity: A Summary Of 25 Postmortem Cases

Jin, Ming, Shi, Run Zhang, Gock, Susan B, Jannetto, Paul J, Jentzen, Jeffrey M, Wong, Steven H

Journal:

Therapeutic Drug Monitoring

Year:

2005

Language:

english

File:

PDF, 691 KB

english, 2005

38

Medical Complications of Cocaine Abuse

Jentzen, Jeffrey

Journal:

American Journal of Clinical Pathology

Year:

1993

Language:

english

File:

PDF, 256 KB

english, 1993

39

Sudden Death Associated With Campylobacter Jejuni Infection

Jentzen, Jeffrey, Gradus, Steven

Journal:

American Journal of Forensic Medicine & Pathology

Year:

1992

File:

PDF, 98 KB

1992

40

Selecting Forensic Pathology as a Career

Hanzlick, Randy, Prahlow, Joseph A., Denton, Scott, Jentzen, Jeffrey, Quinton, Reade, Sathyavagiswaran, Lakshmanan, Utley, Suzanne

Journal:

American Journal of Forensic Medicine & Pathology

Year:

2008

Language:

english

File:

PDF, 1.14 MB

english, 2008

41

Taylor Approximations for Stochastic Partial Differential Equations || 2. Taylor Expansions and Numerical Schemes for RODEs

Jentzen, Arnulf, Kloeden, Peter E.

Year:

2011

Language:

english

File:

PDF, 151 KB

english, 2011

42

Taylor Approximations for Stochastic Partial Differential Equations || Front Matter

Jentzen, Arnulf, Kloeden, Peter E.

Year:

2011

Language:

english

File:

PDF, 197 KB

english, 2011

43

Taylor Approximations for Stochastic Partial Differential Equations || 1. Introduction

Jentzen, Arnulf, Kloeden, Peter E.

Year:

2011

Language:

english

File:

PDF, 80 KB

english, 2011

44

Taylor Approximations for Stochastic Partial Differential Equations || 4. Numerical Methods for SODEs with Nonstandard Assumptions

Jentzen, Arnulf, Kloeden, Peter E.

Year:

2011

Language:

english

File:

PDF, 116 KB

english, 2011

45

Taylor Approximations for Stochastic Partial Differential Equations || 3. SODEs

Jentzen, Arnulf, Kloeden, Peter E.

Year:

2011

Language:

english

File:

PDF, 151 KB

english, 2011

46

Taylor Approximations for Stochastic Partial Differential Equations || Appendix A: Regularity Estimates for SPDEs

Jentzen, Arnulf, Kloeden, Peter E.

Year:

2011

Language:

english

File:

PDF, 291 KB

english, 2011

47

Renormalized powers of Ornstein–Uhlenbeck processes and well-posedness of stochastic Ginzburg–Landau equations

E, Weinan, Jentzen, Arnulf, Shen, Hao

Journal:

Nonlinear Analysis: Theory, Methods & Applications

Year:

2016

Language:

english

File:

PDF, 919 KB

english, 2016

48

Loss of regularity for Kolmogorov equations

Hairer, Martin, Hutzenthaler, Martin, Jentzen, Arnulf

Journal:

The Annals of Probability

Year:

2015

Language:

english

File:

PDF, 584 KB

english, 2015

49

A Retrospective Study of the Investigation of Homicidal Childhood Asphyxial Deaths

Brown, Theodore T., Batalis, Nick I., McClain, Joni L., Corey, Tracey, Collins, Kim A., Jentzen, Jeffrey M., Prahlow, Joseph A.

Journal:

Journal of Forensic Sciences

Year:

2017

Language:

english

File:

PDF, 117 KB

english, 2017

50

Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations

Hutzenthaler, Martin, Jentzen, Arnulf, Wang, Xiaojie

Journal:

Mathematics of Computation

Year:

2017

Language:

english

File:

PDF, 733 KB

english, 2017

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