Minh-Thang Do; Hoang-Long Ngo; Nhat-An Pho Tamed-adaptive Euler-Maruyama approximation for SDEs with superlinearly growing and piecewise continuous drift, superlinearly growing and locally Hölder continuous diffusion. (English) Zbl 07820044 J. Complexity 82, Article ID 101833, 40 p. (2024). MSC: 65C30 60H35 PDFBibTeX XMLCite \textit{Minh-Thang Do} et al., J. Complexity 82, Article ID 101833, 40 p. (2024; Zbl 07820044) Full Text: DOI arXiv
Ellinger, Simon Sharp lower error bounds for strong approximation of SDEs with piecewise Lipschitz continuous drift coefficient. (English) Zbl 07805477 J. Complexity 81, Article ID 101822, 29 p. (2024). MSC: 60Hxx 65Cxx 65Lxx PDFBibTeX XMLCite \textit{S. Ellinger}, J. Complexity 81, Article ID 101822, 29 p. (2024; Zbl 07805477) Full Text: DOI arXiv
Becker, Sebastian; Jentzen, Arnulf; Müller, Marvin S.; von Wurstemberger, Philippe Learning the random variables in Monte Carlo simulations with stochastic gradient descent: machine learning for parametric PDEs and financial derivative pricing. (English) Zbl 07790868 Math. Finance 34, No. 1, 90-150 (2024). Reviewer: Nikolay Kyurkchiev (Plovdiv) MSC: 91G60 65C05 65C30 91G20 PDFBibTeX XMLCite \textit{S. Becker} et al., Math. Finance 34, No. 1, 90--150 (2024; Zbl 07790868) Full Text: DOI arXiv OA License
Kirchner, Kristin; Schwab, Christoph Monte Carlo convergence rates for \(k\)th moments in Banach spaces. (English) Zbl 07784448 J. Funct. Anal. 286, No. 3, Article ID 110218, 58 p. (2024). MSC: 65C05 46A32 60B11 60H35 PDFBibTeX XMLCite \textit{K. Kirchner} and \textit{C. Schwab}, J. Funct. Anal. 286, No. 3, Article ID 110218, 58 p. (2024; Zbl 07784448) Full Text: DOI arXiv
Beck, Christian; Becker, Sebastian; Cheridito, Patrick; Jentzen, Arnulf; Neufeld, Ariel An efficient Monte Carlo scheme for Zakai equations. (English) Zbl 07758890 Commun. Nonlinear Sci. Numer. Simul. 126, Article ID 107438, 27 p. (2023). MSC: 93E11 93C20 60H15 PDFBibTeX XMLCite \textit{C. Beck} et al., Commun. Nonlinear Sci. Numer. Simul. 126, Article ID 107438, 27 p. (2023; Zbl 07758890) Full Text: DOI arXiv
Buczolich, Zoltán; Leobacher, Gunther; Steinicke, Alexander Continuous functions with impermeable graphs. (English) Zbl 07750741 Math. Nachr. 296, No. 10, 4778-4805 (2023). MSC: 26A16 28A78 26A21 26B30 26B35 54C05 54E40 PDFBibTeX XMLCite \textit{Z. Buczolich} et al., Math. Nachr. 296, No. 10, 4778--4805 (2023; Zbl 07750741) Full Text: DOI arXiv OA License
Deaconu, Madalina; Herrmann, Samuel Strong approximation of Bessel processes. (English) Zbl 1514.65006 Methodol. Comput. Appl. Probab. 25, No. 1, Paper No. 11, 24 p. (2023). MSC: 65C05 60J60 60J25 60G17 60G50 PDFBibTeX XMLCite \textit{M. Deaconu} and \textit{S. Herrmann}, Methodol. Comput. Appl. Probab. 25, No. 1, Paper No. 11, 24 p. (2023; Zbl 1514.65006) Full Text: DOI arXiv
Dareiotis, Konstantinos; Gerencsér, Máté; Lê, Khoa Quantifying a convergence theorem of Gyöngy and Krylov. (English) Zbl 1511.60102 Ann. Appl. Probab. 33, No. 3, 2291-2323 (2023). MSC: 60H35 65C30 60H10 60H50 PDFBibTeX XMLCite \textit{K. Dareiotis} et al., Ann. Appl. Probab. 33, No. 3, 2291--2323 (2023; Zbl 1511.60102) Full Text: DOI arXiv
Müller-Gronbach, Thomas; Yaroslavtseva, Larisa Sharp lower error bounds for strong approximation of SDEs with discontinuous drift coefficient by coupling of noise. (English) Zbl 1515.65031 Ann. Appl. Probab. 33, No. 2, 1102-1135 (2023). MSC: 65C30 60H10 60H35 PDFBibTeX XMLCite \textit{T. Müller-Gronbach} and \textit{L. Yaroslavtseva}, Ann. Appl. Probab. 33, No. 2, 1102--1135 (2023; Zbl 1515.65031) Full Text: DOI arXiv
Sönmez, Ercan On mixed fractional stochastic differential equations with discontinuous drift coefficient. (English) Zbl 1516.60034 J. Appl. Probab. 60, No. 2, 589-606 (2023). MSC: 60H10 65C30 60H99 PDFBibTeX XMLCite \textit{E. Sönmez}, J. Appl. Probab. 60, No. 2, 589--606 (2023; Zbl 1516.60034) Full Text: DOI arXiv
Butkovsky, Oleg; Dareiotis, Konstantinos; Gerencsér, Máté Optimal rate of convergence for approximations of SPDEs with nonregular drift. (English) Zbl 1514.60072 SIAM J. Numer. Anal. 61, No. 2, 1103-1137 (2023). Reviewer: Alexandra Rodkina (College Station) MSC: 60H15 60H50 60H35 35R60 35K57 PDFBibTeX XMLCite \textit{O. Butkovsky} et al., SIAM J. Numer. Anal. 61, No. 2, 1103--1137 (2023; Zbl 1514.60072) Full Text: DOI arXiv
Taguchi, Dai On the strong convergence rate for the Euler-Maruyama scheme of one-dimensional SDEs with irregular diffusion coefficient and local time. (English) Zbl 1504.65018 J. Complexity 74, Article ID 101695, 17 p. (2023). MSC: 65C30 60H35 41A25 PDFBibTeX XMLCite \textit{D. Taguchi}, J. Complexity 74, Article ID 101695, 17 p. (2023; Zbl 1504.65018) Full Text: DOI
Leobacher, Gunther; Reisinger, Christoph; Stockinger, Wolfgang Well-posedness and numerical schemes for one-dimensional McKean-Vlasov equations and interacting particle systems with discontinuous drift. (English) Zbl 1504.65017 BIT 62, No. 4, 1505-1549 (2022). MSC: 65C30 60H30 60H35 60K35 60K40 PDFBibTeX XMLCite \textit{G. Leobacher} et al., BIT 62, No. 4, 1505--1549 (2022; Zbl 1504.65017) Full Text: DOI arXiv
De Angelis, Tiziano; Germain, Maximilien; Issoglio, Elena A numerical scheme for stochastic differential equations with distributional drift. (English) Zbl 1500.65001 Stochastic Processes Appl. 154, 55-90 (2022). MSC: 65C30 60H10 60H35 60J60 PDFBibTeX XMLCite \textit{T. De Angelis} et al., Stochastic Processes Appl. 154, 55--90 (2022; Zbl 1500.65001) Full Text: DOI arXiv
Jentzen, Arnulf; Kuckuck, Benno; Müller-Gronbach, Thomas; Yaroslavtseva, Larisa Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven stochastic differential equations with smooth drift coefficient functions with at most polynomially growing derivatives. (English) Zbl 1498.60218 Discrete Contin. Dyn. Syst., Ser. B 27, No. 7, 3707-3724 (2022). MSC: 60H10 PDFBibTeX XMLCite \textit{A. Jentzen} et al., Discrete Contin. Dyn. Syst., Ser. B 27, No. 7, 3707--3724 (2022; Zbl 1498.60218) Full Text: DOI arXiv
Eisenmann, Monika; Kovács, Mihály; Kruse, Raphael; Larsson, Stig Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations. (English) Zbl 1496.65009 BIT 62, No. 3, 803-848 (2022). MSC: 65C30 60H10 34F05 60H35 PDFBibTeX XMLCite \textit{M. Eisenmann} et al., BIT 62, No. 3, 803--848 (2022; Zbl 1496.65009) Full Text: DOI arXiv
Bencheikh, Oumaima; Jourdain, Benjamin Convergence in total variation of the Euler-Maruyama scheme applied to diffusion processes with measurable drift coefficient and additive noise. (English) Zbl 1506.65019 SIAM J. Numer. Anal. 60, No. 4, 1701-1740 (2022). MSC: 65C30 65C05 60H35 PDFBibTeX XMLCite \textit{O. Bencheikh} and \textit{B. Jourdain}, SIAM J. Numer. Anal. 60, No. 4, 1701--1740 (2022; Zbl 1506.65019) Full Text: DOI arXiv
Bao, Jianhai; Huang, Xing; Zhang, Shao-Qin Convergence rate of the EM algorithm for SDEs with low regular drifts. (English) Zbl 1496.60061 J. Appl. Probab. 59, No. 2, 447-470 (2022). MSC: 60H10 65C30 60H35 PDFBibTeX XMLCite \textit{J. Bao} et al., J. Appl. Probab. 59, No. 2, 447--470 (2022; Zbl 1496.60061) Full Text: DOI
Suo, Yongqiang; Yuan, Chenggui; Zhang, Shao-Qin Weak convergence of Euler scheme for SDEs with low regular drift. (English) Zbl 1496.65011 Numer. Algorithms 90, No. 2, 731-747 (2022). MSC: 65C30 60H10 60H35 PDFBibTeX XMLCite \textit{Y. Suo} et al., Numer. Algorithms 90, No. 2, 731--747 (2022; Zbl 1496.65011) Full Text: DOI arXiv
Altmeyer, Randolf; Le Guével, Ronan Optimal \(L^2\)-approximation of occupation and local times for symmetric stable processes. (English) Zbl 07524987 Electron. J. Stat. 16, No. 1, 2859-2883 (2022). MSC: 62-XX PDFBibTeX XMLCite \textit{R. Altmeyer} and \textit{R. Le Guével}, Electron. J. Stat. 16, No. 1, 2859--2883 (2022; Zbl 07524987) Full Text: DOI arXiv Link
Yaroslavtseva, Larisa An adaptive strong order 1 method for SDEs with discontinuous drift coefficient. (English) Zbl 1492.65029 J. Math. Anal. Appl. 513, No. 2, Article ID 126180, 29 p. (2022). MSC: 65C30 60H10 60H35 PDFBibTeX XMLCite \textit{L. Yaroslavtseva}, J. Math. Anal. Appl. 513, No. 2, Article ID 126180, 29 p. (2022; Zbl 1492.65029) Full Text: DOI arXiv
Arlazarov, Vladimir Viktorovich; Voĭsyat, Yuliya Sergeevich; Matalov, Daniil Pavlovich; Nikolaev, Dmitriĭ Petrovich; Usilin, Sergeĭ Aleksandrovich Evolution of the Viola-Jones object detection method: a survey. (English) Zbl 1524.68341 Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model. Program. 14, No. 4, 5-23 (2021). MSC: 68T10 68T05 68T45 PDFBibTeX XMLCite \textit{V. V. Arlazarov} et al., Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model. Program. 14, No. 4, 5--23 (2021; Zbl 1524.68341) Full Text: DOI MNR
Butkovsky, Oleg; Dareiotis, Konstantinos; Gerencsér, Máté Approximation of SDEs: a stochastic sewing approach. (English) Zbl 1490.60211 Probab. Theory Relat. Fields 181, No. 4, 975-1034 (2021). MSC: 60H50 60H10 65C30 PDFBibTeX XMLCite \textit{O. Butkovsky} et al., Probab. Theory Relat. Fields 181, No. 4, 975--1034 (2021; Zbl 1490.60211) Full Text: DOI arXiv
Przybyłowicz, Paweł; Szölgyenyi, Michaela Existence, uniqueness, and approximation of solutions of jump-diffusion SDEs with discontinuous drift. (English) Zbl 1510.65018 Appl. Math. Comput. 403, Article ID 126191, 15 p. (2021). MSC: 65C30 60H10 PDFBibTeX XMLCite \textit{P. Przybyłowicz} and \textit{M. Szölgyenyi}, Appl. Math. Comput. 403, Article ID 126191, 15 p. (2021; Zbl 1510.65018) Full Text: DOI arXiv
Jentzen, Arnulf; Kuckuck, Benno; Müller-Gronbach, Thomas; Yaroslavtseva, Larisa On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values. (English) Zbl 1471.34116 J. Math. Anal. Appl. 502, No. 2, Article ID 125240, 23 p. (2021). Reviewer: Melvin D. Lax (Long Beach) MSC: 34F05 34A12 65P99 PDFBibTeX XMLCite \textit{A. Jentzen} et al., J. Math. Anal. Appl. 502, No. 2, Article ID 125240, 23 p. (2021; Zbl 1471.34116) Full Text: DOI arXiv
Dareiotis, Konstantinos; Gerencsér, Máté On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. (English) Zbl 1459.60144 Electron. J. Probab. 25, Paper No. 82, 18 p. (2020). MSC: 60H35 60H10 65C30 PDFBibTeX XMLCite \textit{K. Dareiotis} and \textit{M. Gerencsér}, Electron. J. Probab. 25, Paper No. 82, 18 p. (2020; Zbl 1459.60144) Full Text: DOI arXiv Euclid
Hatzesberger, Simon Strongly asymptotically optimal schemes for the strong approximation of stochastic differential equations with respect to the supremum error. (English) Zbl 1469.65030 J. Complexity 60, Article ID 101496, 26 p. (2020). MSC: 65C30 60H35 60H10 91G60 PDFBibTeX XMLCite \textit{S. Hatzesberger}, J. Complexity 60, Article ID 101496, 26 p. (2020; Zbl 1469.65030) Full Text: DOI arXiv
Müller-Gronbach, Thomas; Yaroslavtseva, Larisa On the performance of the Euler-Maruyama scheme for SDEs with discontinuous drift coefficient. (English. French summary) Zbl 1494.65006 Ann. Inst. Henri Poincaré, Probab. Stat. 56, No. 2, 1162-1178 (2020). Reviewer: Nikolaos Halidias (Athína) MSC: 65C30 60H10 60H35 PDFBibTeX XMLCite \textit{T. Müller-Gronbach} and \textit{L. Yaroslavtseva}, Ann. Inst. Henri Poincaré, Probab. Stat. 56, No. 2, 1162--1178 (2020; Zbl 1494.65006) Full Text: DOI arXiv Euclid
Hoel, H.; Karlsen, K. H.; Risebro, N. H.; Storrøsten, E. B. Numerical methods for conservation laws with rough flux. (English) Zbl 1437.35485 Stoch. Partial Differ. Equ., Anal. Comput. 8, No. 1, 186-261 (2020). MSC: 35L65 35A35 65M06 60H15 65C30 PDFBibTeX XMLCite \textit{H. Hoel} et al., Stoch. Partial Differ. Equ., Anal. Comput. 8, No. 1, 186--261 (2020; Zbl 1437.35485) Full Text: DOI arXiv
Göttlich, S.; Lux, K.; Neuenkirch, A. The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate. (English) Zbl 1487.65009 Adv. Difference Equ. 2019, Paper No. 429, 21 p. (2019). MSC: 65C30 60H10 60H35 65L20 PDFBibTeX XMLCite \textit{S. Göttlich} et al., Adv. Difference Equ. 2019, Paper No. 429, 21 p. (2019; Zbl 1487.65009) Full Text: DOI arXiv
Ngo, Hoang-Long; Taguchi, Dai On the Euler-Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients. (English) Zbl 07316680 Math. Comput. Simul. 161, 102-112 (2019). MSC: 60Hxx PDFBibTeX XMLCite \textit{H.-L. Ngo} and \textit{D. Taguchi}, Math. Comput. Simul. 161, 102--112 (2019; Zbl 07316680) Full Text: DOI
Aurzada, Frank; Lifshits, Mikhail How complex is a random picture? (English) Zbl 1422.60008 J. Complexity 53, 133-161 (2019). MSC: 60B05 60G55 60F10 PDFBibTeX XMLCite \textit{F. Aurzada} and \textit{M. Lifshits}, J. Complexity 53, 133--161 (2019; Zbl 1422.60008) Full Text: DOI arXiv
Bao, Jianhai; Huang, Xing; Yuan, Chenggui Convergence rate of Euler-Maruyama scheme for SDEs with Hölder-Dini continuous drifts. (English) Zbl 1433.60072 J. Theor. Probab. 32, No. 2, 848-871 (2019). MSC: 60H35 41A25 60H10 PDFBibTeX XMLCite \textit{J. Bao} et al., J. Theor. Probab. 32, No. 2, 848--871 (2019; Zbl 1433.60072) Full Text: DOI arXiv
Hefter, Mario; Herzwurm, André; Müller-Gronbach, Thomas Lower error bounds for strong approximation of scalar SDEs with non-Lipschitzian coefficients. (English) Zbl 07039124 Ann. Appl. Probab. 29, No. 1, 178-216 (2019). MSC: 65C30 60H10 PDFBibTeX XMLCite \textit{M. Hefter} et al., Ann. Appl. Probab. 29, No. 1, 178--216 (2019; Zbl 07039124) Full Text: DOI arXiv Euclid
Neuenkirch, Andreas; Szölgyenyi, Michaela; Szpruch, Lukasz An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis. (English) Zbl 1418.60062 SIAM J. Numer. Anal. 57, No. 1, 378-403 (2019). MSC: 60H10 65C30 65C20 65L20 PDFBibTeX XMLCite \textit{A. Neuenkirch} et al., SIAM J. Numer. Anal. 57, No. 1, 378--403 (2019; Zbl 1418.60062) Full Text: DOI arXiv
Hefter, Mario; Jentzen, Arnulf On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes. (English) Zbl 1425.91401 Finance Stoch. 23, No. 1, 139-172 (2019). Reviewer: Nikolay Kyurkchiev (Plovdiv) MSC: 91G20 91G30 60H10 PDFBibTeX XMLCite \textit{M. Hefter} and \textit{A. Jentzen}, Finance Stoch. 23, No. 1, 139--172 (2019; Zbl 1425.91401) Full Text: DOI arXiv
Jentzen, Arnulf; Salimova, Diyora; Welti, Timo Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations. (English) Zbl 1403.60059 J. Math. Anal. Appl. 469, No. 2, 661-704 (2019). MSC: 60H35 60H15 35Q53 65C30 PDFBibTeX XMLCite \textit{A. Jentzen} et al., J. Math. Anal. Appl. 469, No. 2, 661--704 (2019; Zbl 1403.60059) Full Text: DOI arXiv
Cozma, Andrei; Reisinger, Christoph Strong convergence rates for Euler approximations to a class of stochastic path-dependent volatility models. (English) Zbl 1433.60074 SIAM J. Numer. Anal. 56, No. 6, 3430-3458 (2018). MSC: 60H35 65C05 65C30 91G20 91G30 PDFBibTeX XMLCite \textit{A. Cozma} and \textit{C. Reisinger}, SIAM J. Numer. Anal. 56, No. 6, 3430--3458 (2018; Zbl 1433.60074) Full Text: DOI arXiv
Gobet, Emmanuel; Stazhynski, Uladzislau Optimal discretization of stochastic integrals driven by general Brownian semimartingale. (English. French summary) Zbl 1404.60055 Ann. Inst. Henri Poincaré, Probab. Stat. 54, No. 3, 1556-1582 (2018). MSC: 60G40 60F15 60H05 PDFBibTeX XMLCite \textit{E. Gobet} and \textit{U. Stazhynski}, Ann. Inst. Henri Poincaré, Probab. Stat. 54, No. 3, 1556--1582 (2018; Zbl 1404.60055) Full Text: DOI Euclid
Müller-Gronbach, Thomas; Yaroslavtseva, Larisa A note on strong approximation of SDEs with smooth coefficients that have at most linearly growing derivatives. (English) Zbl 06925396 J. Math. Anal. Appl. 467, No. 2, 1013-1031 (2018). MSC: 65Cxx 60-XX PDFBibTeX XMLCite \textit{T. Müller-Gronbach} and \textit{L. Yaroslavtseva}, J. Math. Anal. Appl. 467, No. 2, 1013--1031 (2018; Zbl 06925396) Full Text: DOI arXiv
Leobacher, Gunther; Szölgyenyi, Michaela Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient. (English) Zbl 1432.65012 Numer. Math. 138, No. 1, 219-239 (2018). MSC: 65C30 60H10 60H35 34F05 65L20 PDFBibTeX XMLCite \textit{G. Leobacher} and \textit{M. Szölgyenyi}, Numer. Math. 138, No. 1, 219--239 (2018; Zbl 1432.65012) Full Text: DOI arXiv
Belomestny, Denis; Häfner, Stefan; Nagapetyan, Tigran; Urusov, Mikhail Variance reduction for discretised diffusions via regression. (English) Zbl 1373.93303 J. Math. Anal. Appl. 458, No. 1, 393-418 (2018). MSC: 93E03 60H10 65C05 PDFBibTeX XMLCite \textit{D. Belomestny} et al., J. Math. Anal. Appl. 458, No. 1, 393--418 (2018; Zbl 1373.93303) Full Text: DOI arXiv
Gerencsér, Máté; Jentzen, Arnulf; Salimova, Diyora On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions. (English) Zbl 1404.60082 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2207, Article ID 20170104, 16 p. (2017). MSC: 60H10 34F05 PDFBibTeX XMLCite \textit{M. Gerencsér} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2207, Article ID 20170104, 16 p. (2017; Zbl 1404.60082) Full Text: DOI arXiv
Belomestny, Denis; Häfner, Stefan; Urusov, Mikhail Truncated control variates for weak approximation schemes. (English) Zbl 1384.65037 ESAIM, Proc. Surv. 59, 15-42 (2017). MSC: 65K10 93B40 65Y20 PDFBibTeX XMLCite \textit{D. Belomestny} et al., ESAIM, Proc. Surv. 59, 15--42 (2017; Zbl 1384.65037) Full Text: DOI arXiv
Kloeden, Peter; Shardlow, Tony Gauss-quadrature method for one-dimensional mean-field SDEs. (English) Zbl 1378.65035 SIAM J. Sci. Comput. 39, No. 6, A2784-A2807 (2017). MSC: 65C30 60H10 34F05 60H35 PDFBibTeX XMLCite \textit{P. Kloeden} and \textit{T. Shardlow}, SIAM J. Sci. Comput. 39, No. 6, A2784--A2807 (2017; Zbl 1378.65035) Full Text: DOI arXiv
Ngo, Hoang-Long; Taguchi, Dai Strong convergence for the Euler-Maruyama approximation of stochastic differential equations with discontinuous coefficients. (English) Zbl 1386.60242 Stat. Probab. Lett. 125, 55-63 (2017). MSC: 60H35 41A25 65C30 PDFBibTeX XMLCite \textit{H.-L. Ngo} and \textit{D. Taguchi}, Stat. Probab. Lett. 125, 55--63 (2017; Zbl 1386.60242) Full Text: DOI arXiv
Yaroslavtseva, Larisa On non-polynomial lower error bounds for adaptive strong approximation of SDEs. (English) Zbl 1396.65012 J. Complexity 42, 1-18 (2017). MSC: 65C30 65Y20 PDFBibTeX XMLCite \textit{L. Yaroslavtseva}, J. Complexity 42, 1--18 (2017; Zbl 1396.65012) Full Text: DOI arXiv
Yaroslavtseva, Larisa; Müller-Gronbach, Thomas On sub-polynomial lower error bounds for quadrature of SDEs with bounded smooth coefficients. (English) Zbl 1369.65012 Stochastic Anal. Appl. 35, No. 3, 423-451 (2017). Reviewer: Melvin D. Lax (Long Beach) MSC: 65C30 60H35 60H10 34F05 60J65 PDFBibTeX XMLCite \textit{L. Yaroslavtseva} and \textit{T. Müller-Gronbach}, Stochastic Anal. Appl. 35, No. 3, 423--451 (2017; Zbl 1369.65012) Full Text: DOI arXiv
Müller-Gronbach, Thomas; Yaroslavtseva, Larisa Deterministic quadrature formulas for SDEs based on simplified weak Itô-Taylor steps. (English) Zbl 1382.65023 Found. Comput. Math. 16, No. 5, 1325-1366 (2016). Reviewer: Philipp Dörsek (London) MSC: 65C30 60H35 60H10 34F05 PDFBibTeX XMLCite \textit{T. Müller-Gronbach} and \textit{L. Yaroslavtseva}, Found. Comput. Math. 16, No. 5, 1325--1366 (2016; Zbl 1382.65023) Full Text: DOI
Halidias, Nikolaos On the construction of boundary preserving numerical schemes. (English) Zbl 1351.60072 Monte Carlo Methods Appl. 22, No. 4, 277-289 (2016). MSC: 60H10 60H35 PDFBibTeX XMLCite \textit{N. Halidias}, Monte Carlo Methods Appl. 22, No. 4, 277--289 (2016; Zbl 1351.60072) Full Text: DOI arXiv
Anderson, David F.; Higham, Desmond J.; Sun, Yu Multilevel Monte Carlo for stochastic differential equations with small noise. (English) Zbl 1334.60128 SIAM J. Numer. Anal. 54, No. 2, 505-529 (2016). MSC: 60H35 60H10 65C05 65C30 PDFBibTeX XMLCite \textit{D. F. Anderson} et al., SIAM J. Numer. Anal. 54, No. 2, 505--529 (2016; Zbl 1334.60128) Full Text: DOI arXiv
Müller-Gronbach, Thomas; Ritter, Klaus; Yaroslavtseva, Larisa On the complexity of computing quadrature formulas for marginal distributions of SDEs. (English) Zbl 1304.65010 J. Complexity 31, No. 1, 110-145 (2015). MSC: 65C30 60H10 60H35 34F05 65Y20 65L20 PDFBibTeX XMLCite \textit{T. Müller-Gronbach} et al., J. Complexity 31, No. 1, 110--145 (2015; Zbl 1304.65010) Full Text: DOI
Altmayer, Martin; Dereich, Steffen; Li, Sangmeng; Müller-Gronbach, Thomas; Neuenkirch, Andreas; Ritter, Klaus; Yaroslavtseva, Larisa Constructive quantization and multilevel algorithms for quadrature of stochastic differential equations. (English) Zbl 1317.65029 Dahlke, Stephan (ed.) et al., Extraction of quantifiable information from complex systems. Cham: Springer (ISBN 978-3-319-08158-8/hbk; 978-3-319-08159-5/ebook). Lecture Notes in Computational Science and Engineering 102, 109-132 (2014). MSC: 65C30 60H10 60H35 65C05 34F05 PDFBibTeX XMLCite \textit{M. Altmayer} et al., Lect. Notes Comput. Sci. Eng. 102, 109--132 (2014; Zbl 1317.65029) Full Text: DOI
Müller-Gronbach, Thomas; Ritter, Klaus A local refinement strategy for constructive quantization of scalar SDEs. (English) Zbl 1292.65003 Found. Comput. Math. 13, No. 6, 1005-1033 (2013). MSC: 65C30 60H10 PDFBibTeX XMLCite \textit{T. Müller-Gronbach} and \textit{K. Ritter}, Found. Comput. Math. 13, No. 6, 1005--1033 (2013; Zbl 1292.65003) Full Text: DOI
Dereich, Steffen; Scheutzow, Michael; Schottstedt, Reik Constructive quantization: approximation by empirical measures. (English. French summary) Zbl 1283.60063 Ann. Inst. Henri Poincaré, Probab. Stat. 49, No. 4, 1183-1203 (2013). Reviewer: Ludger Rüschendorf (Freiburg i. Br.) MSC: 60F25 65D32 PDFBibTeX XMLCite \textit{S. Dereich} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 49, No. 4, 1183--1203 (2013; Zbl 1283.60063) Full Text: DOI arXiv Euclid