Addona, Davide; Lorenzi, Luca; Tessitore, Gianmario Regularity results for nonlinear Young equations and applications. (English) Zbl 1485.35439 J. Evol. Equ. 22, No. 1, Paper No. 3, 34 p. (2022). MSC: 35R60 35C15 35B65 60H05 60H15 47D06 PDF BibTeX XML Cite \textit{D. Addona} et al., J. Evol. Equ. 22, No. 1, Paper No. 3, 34 p. (2022; Zbl 1485.35439) Full Text: DOI arXiv
Brault, Antoine; Lejay, Antoine The non-linear sewing lemma. II. Lipschitz continuous formulation. (English) Zbl 1471.60162 J. Differ. Equations 293, 482-519 (2021). MSC: 60L20 60H10 37N25 PDF BibTeX XML Cite \textit{A. Brault} and \textit{A. Lejay}, J. Differ. Equations 293, 482--519 (2021; Zbl 1471.60162) Full Text: DOI arXiv Link
Hocquet, Antoine; Nilssen, Torstein An Itô formula for rough partial differential equations and some applications. (English) Zbl 1477.60148 Potential Anal. 54, No. 2, 331-386 (2021). Reviewer: David Prömel (Mannheim) MSC: 60L50 60H15 35D30 PDF BibTeX XML Cite \textit{A. Hocquet} and \textit{T. Nilssen}, Potential Anal. 54, No. 2, 331--386 (2021; Zbl 1477.60148) Full Text: DOI arXiv
Besalú, Mireia; Binotto, Giulia; Rovira, Carles Convergence of delay equations driven by a Hölder continuous function of order \(1/3<\beta<1/2\). (English) Zbl 1472.60092 Electron. J. Differ. Equ. 2020, Paper No. 65, 27 p. (2020). Reviewer: Nikolaos Halidias (Athína) MSC: 60H10 60H07 PDF BibTeX XML Cite \textit{M. Besalú} et al., Electron. J. Differ. Equ. 2020, Paper No. 65, 27 p. (2020; Zbl 1472.60092) Full Text: arXiv Link
Lopusanschi, Olga; Simon, Damien Lévy area with a drift as a renormalization limit of Markov chains on periodic graphs. (English) Zbl 1396.60076 Stochastic Processes Appl. 128, No. 7, 2404-2426 (2018). MSC: 60H30 60F17 60J10 60J65 PDF BibTeX XML Cite \textit{O. Lopusanschi} and \textit{D. Simon}, Stochastic Processes Appl. 128, No. 7, 2404--2426 (2018; Zbl 1396.60076) Full Text: DOI arXiv
Garrido-Atienza, María J.; Neuenkirch, Andreas; Schmalfuß, Björn Asymptotical stability of differential equations driven by Hölder continuous paths. (English) Zbl 1452.37060 J. Dyn. Differ. Equations 30, No. 1, 359-377 (2018). MSC: 37H30 60G22 34F05 60H10 PDF BibTeX XML Cite \textit{M. J. Garrido-Atienza} et al., J. Dyn. Differ. Equations 30, No. 1, 359--377 (2018; Zbl 1452.37060) Full Text: DOI arXiv
Coutin, Laure; Lejay, Antoine Sensitivity of rough differential equations: an approach through the omega lemma. (English) Zbl 1423.60088 J. Differ. Equations 264, No. 6, 3899-3917 (2018). Reviewer: Nikolaos Halidias (Athens) MSC: 60H10 60H07 60H05 PDF BibTeX XML Cite \textit{L. Coutin} and \textit{A. Lejay}, J. Differ. Equations 264, No. 6, 3899--3917 (2018; Zbl 1423.60088) Full Text: DOI arXiv
Samsonyuk, Ol’ga Nikolaevna; Staritsyn, Maksim Vladimirovich Impulsive control systems with trajectories of bounded \(p\)-variation. (Russian. English summary) Zbl 1364.93350 Izv. Irkutsk. Gos. Univ., Ser. Mat. 19, 164-177 (2017). MSC: 93C10 93C23 49N25 PDF BibTeX XML Cite \textit{O. N. Samsonyuk} and \textit{M. V. Staritsyn}, Izv. Irkutsk. Gos. Univ., Ser. Mat. 19, 164--177 (2017; Zbl 1364.93350) Full Text: Link
Flint, Guy; Hambly, Ben; Lyons, Terry Discretely sampled signals and the rough Hoff process. (English) Zbl 1348.60058 Stochastic Processes Appl. 126, No. 9, 2593-2614 (2016). MSC: 60G17 60G35 60G44 60H10 PDF BibTeX XML Cite \textit{G. Flint} et al., Stochastic Processes Appl. 126, No. 9, 2593--2614 (2016; Zbl 1348.60058) Full Text: DOI arXiv
Aronna, M. Soledad; Rampazzo, Franco \(\mathcal{L}^1\) limit solutions for control systems. (English) Zbl 1323.34076 J. Differ. Equations 258, No. 3, 954-979 (2015). Reviewer: Didier Henrion (Toulouse) MSC: 34H05 34A12 93C15 PDF BibTeX XML Cite \textit{M. S. Aronna} and \textit{F. Rampazzo}, J. Differ. Equations 258, No. 3, 954--979 (2015; Zbl 1323.34076) Full Text: DOI arXiv
Coutin, Laure; Lejay, Antoine Perturbed linear rough differential equations. (English. French summary) Zbl 1322.60084 Ann. Math. Blaise Pascal 21, No. 1, 103-150 (2014). Reviewer: Dominique Lepingle (Orléans) MSC: 60H10 34A25 PDF BibTeX XML Cite \textit{L. Coutin} and \textit{A. Lejay}, Ann. Math. Blaise Pascal 21, No. 1, 103--150 (2014; Zbl 1322.60084) Full Text: DOI
Besalú, Mireia; Márquez-Carreras, David; Rovira, Carles Delay equations with non-negativity constraints driven by a Hölder continuous function of order \(\beta\in\left(\frac{1}{3},\frac{1}{2}\right)\). (English) Zbl 1302.60087 Potential Anal. 41, No. 1, 117-141 (2014). Reviewer: Anna Karczewska (Zielona Gora) MSC: 60H05 PDF BibTeX XML Cite \textit{M. Besalú} et al., Potential Anal. 41, No. 1, 117--141 (2014; Zbl 1302.60087) Full Text: DOI
Inahama, Yuzuru Malliavin differentiability of solutions of rough differential equations. (English) Zbl 1296.60142 J. Funct. Anal. 267, No. 5, 1566-1584 (2014). MSC: 60H07 60H99 60G15 PDF BibTeX XML Cite \textit{Y. Inahama}, J. Funct. Anal. 267, No. 5, 1566--1584 (2014; Zbl 1296.60142) Full Text: DOI arXiv
Unterberger, Jérémie A renormalized rough path over fractional Brownian motion. (English) Zbl 1276.60048 Commun. Math. Phys. 320, No. 3, 603-636 (2013). Reviewer: Akira Asada (Takarazuka) MSC: 60G22 60J65 26A16 58D30 81T15 PDF BibTeX XML Cite \textit{J. Unterberger}, Commun. Math. Phys. 320, No. 3, 603--636 (2013; Zbl 1276.60048) Full Text: DOI arXiv
Chronopoulou, Alexandra; Tindel, Samy On inference for fractional differential equations. (English) Zbl 1271.62197 Stat. Inference Stoch. Process. 16, No. 1, 29-61 (2013). MSC: 62M09 60H35 60H07 60H10 65C30 PDF BibTeX XML Cite \textit{A. Chronopoulou} and \textit{S. Tindel}, Stat. Inference Stoch. Process. 16, No. 1, 29--61 (2013; Zbl 1271.62197) Full Text: DOI arXiv
Inahama, Yuzuru Laplace approximation for rough differential equation driven by fractional Brownian motion. (English) Zbl 1273.60043 Ann. Probab. 41, No. 1, 170-205 (2013). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60G22 60F17 60H10 PDF BibTeX XML Cite \textit{Y. Inahama}, Ann. Probab. 41, No. 1, 170--205 (2013; Zbl 1273.60043) Full Text: DOI arXiv Euclid
Jorge, León A.; Tindel, Samy Malliavin calculus for fractional delay equations. (English) Zbl 1259.60069 J. Theor. Probab. 25, No. 3, 854-889 (2012). Reviewer: Jacques Franchi (Strasbourg) MSC: 60H20 60H10 60H05 60H07 60G18 60G22 PDF BibTeX XML Cite \textit{L. A. Jorge} and \textit{S. Tindel}, J. Theor. Probab. 25, No. 3, 854--889 (2012; Zbl 1259.60069) Full Text: DOI arXiv
Lejay, Antoine Global solutions to rough differential equations with unbounded vector fields. (English) Zbl 1254.60059 Donati-Martin, Catherine (ed.) et al., Séminaire de Probabilités XLIV. Papers based on the presentations at the 44th séminaire de probabilités, Dijon, France, June 2010. Berlin: Springer (ISBN 978-3-642-27460-2/pbk; 978-3-642-27461-9/ebook). Lecture Notes in Mathematics 2046, 215-246 (2012). Reviewer: Martin Riedler (Wien) MSC: 60H10 60H35 65C30 PDF BibTeX XML Cite \textit{A. Lejay}, Lect. Notes Math. 2046, 215--246 (2012; Zbl 1254.60059) Full Text: DOI Link
Deya, A.; Gubinelli, M.; Tindel, S. Non-linear rough heat equations. (English) Zbl 1255.60106 Probab. Theory Relat. Fields 153, No. 1-2, 97-147 (2012). Reviewer: Constantin Vârsan (Bucureşti) MSC: 60H15 60G22 60H05 PDF BibTeX XML Cite \textit{A. Deya} et al., Probab. Theory Relat. Fields 153, No. 1--2, 97--147 (2012; Zbl 1255.60106) Full Text: DOI arXiv Link
Magnen, Jacques; Unterberger, Jérémie From constructive field theory to fractional stochastic calculus. II: Constructive proof of convergence for the Lévy area of fractional Brownian motion with Hurst index \(\alpha \in \left(\frac{1}{8},\frac{1}{4}\right)\). (English) Zbl 1264.81272 Ann. Henri Poincaré 13, No. 2, 209-270 (2012). Reviewer: Gert Roepstorff (Aachen) MSC: 81T08 60G15 60G20 60H05 60H07 PDF BibTeX XML Cite \textit{J. Magnen} and \textit{J. Unterberger}, Ann. Henri Poincaré 13, No. 2, 209--270 (2012; Zbl 1264.81272) Full Text: DOI arXiv
Magnen, Jacques; Unterberger, Jérémie From constructive field theory to fractional stochastic calculus. I: An introduction: Rough path theory and perturbative heuristics. (English) Zbl 1231.81058 Ann. Henri Poincaré 12, No. 6, 1199-1226 (2011). Reviewer: Adam Skalski (Warszawa) MSC: 81T08 60G17 60G22 60H05 PDF BibTeX XML Cite \textit{J. Magnen} and \textit{J. Unterberger}, Ann. Henri Poincaré 12, No. 6, 1199--1226 (2011; Zbl 1231.81058) Full Text: DOI arXiv
Pagès, Gilles; Sellami, Afef Convergence of multi-dimensional quantized SDEs. (English) Zbl 1236.60056 Donati-Martin, Catherine (ed.) et al., Séminaire de Probabilités XLIII, Poitiers, France, Juin 2009. Berlin: Springer (ISBN 978-3-642-15216-0/pbk; 978-3-642-15217-7/ebook). Lecture Notes in Mathematics 2006, 269-307 (2011). Reviewer: Rainer Buckdahn (Brest) MSC: 60H10 PDF BibTeX XML Cite \textit{G. Pagès} and \textit{A. Sellami}, Lect. Notes Math. 2006, 269--307 (2011; Zbl 1236.60056) Full Text: DOI arXiv
Marty, Renaud; Sølna, Knut A general framework for waves in random media with long-range correlations. (English) Zbl 1223.34085 Ann. Appl. Probab. 21, No. 1, 115-139 (2011). Reviewer: Dora Selesi (Novi Sad) MSC: 34F05 34E10 35R60 37H10 60H20 PDF BibTeX XML Cite \textit{R. Marty} and \textit{K. Sølna}, Ann. Appl. Probab. 21, No. 1, 115--139 (2011; Zbl 1223.34085) Full Text: DOI arXiv
Lejay, Antoine Controlled differential equations as Young integrals: a simple approach. (English) Zbl 1216.34058 J. Differ. Equations 249, No. 8, 1777-1798 (2010). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 34G20 60G22 60H30 PDF BibTeX XML Cite \textit{A. Lejay}, J. Differ. Equations 249, No. 8, 1777--1798 (2010; Zbl 1216.34058) Full Text: DOI Link
Unterberger, Jérémie A rough path over multidimensional fractional Brownian motion with arbitrary Hurst index by Fourier normal ordering. (English) Zbl 1221.05062 Stochastic Processes Appl. 120, No. 8, 1444-1472 (2010). MSC: 05C05 16T05 60F05 60G15 60G18 60H05 PDF BibTeX XML Cite \textit{J. Unterberger}, Stochastic Processes Appl. 120, No. 8, 1444--1472 (2010; Zbl 1221.05062) Full Text: DOI arXiv
Friz, Peter; Victoir, Nicolas Differential equations driven by Gaussian signals. (English) Zbl 1202.60058 Ann. Inst. Henri Poincaré, Probab. Stat. 46, No. 2, 369-413 (2010). Reviewer: Andrew Dale (Durban) MSC: 60G15 60H10 60H99 PDF BibTeX XML Cite \textit{P. Friz} and \textit{N. Victoir}, Ann. Inst. Henri Poincaré, Probab. Stat. 46, No. 2, 369--413 (2010; Zbl 1202.60058) Full Text: DOI arXiv EuDML
Gubinelli, Massimiliano; Tindel, Samy Rough evolution equations. (English) Zbl 1193.60070 Ann. Probab. 38, No. 1, 1-75 (2010). Reviewer: Maria Stolarczyk (Katowice) MSC: 60H05 60H07 60G15 PDF BibTeX XML Cite \textit{M. Gubinelli} and \textit{S. Tindel}, Ann. Probab. 38, No. 1, 1--75 (2010; Zbl 1193.60070) Full Text: DOI arXiv
Gubinelli, Massimiliano Ramification of rough paths. (English) Zbl 1315.60065 J. Differ. Equations 248, No. 4, 693-721 (2010). MSC: 60H05 16T30 PDF BibTeX XML Cite \textit{M. Gubinelli}, J. Differ. Equations 248, No. 4, 693--721 (2010; Zbl 1315.60065) Full Text: DOI arXiv
Bardina, X.; Nourdin, I.; Rovira, C.; Tindel, S. Weak approximation of a fractional SDE. (English) Zbl 1181.60082 Stochastic Processes Appl. 120, No. 1, 39-65 (2010). MSC: 60H10 60H05 PDF BibTeX XML Cite \textit{X. Bardina} et al., Stochastic Processes Appl. 120, No. 1, 39--65 (2010; Zbl 1181.60082) Full Text: DOI arXiv
Coutin, Laure; Victoir, Nicolas Enhanced Gaussian processes and applications. (English) Zbl 1181.60057 ESAIM, Probab. Stat. 13, 247-260 (2009). MSC: 60G15 60G17 PDF BibTeX XML Cite \textit{L. Coutin} and \textit{N. Victoir}, ESAIM, Probab. Stat. 13, 247--260 (2009; Zbl 1181.60057) Full Text: DOI EuDML
Lejay, Antoine Yet another introduction to rough paths. (English) Zbl 1198.60002 Donati-Martin, Catherine (ed.) et al., Séminaire de probabilités XLII. Berlin: Springer (ISBN 978-3-642-01762-9/pbk; 978-3-642-01763-6/ebook). Lecture Notes in Mathematics 1979, 1-101 (2009). Reviewer: Isamu Dôku (Saitama) MSC: 60-01 60Hxx 60H05 58A10 PDF BibTeX XML Cite \textit{A. Lejay}, Lect. Notes Math. 1979, 1--101 (2009; Zbl 1198.60002) Full Text: DOI
Unterberger, Jérémie Stochastic calculus for fractional Brownian motion with Hurst exponent \(H>\frac 1 4 \): A rough path method by analytic extension. (English) Zbl 1172.60007 Ann. Probab. 37, No. 2, 565-614 (2009). Reviewer: A. A. Dorogovtsev (Kyïv) MSC: 60G15 60G17 60H05 PDF BibTeX XML Cite \textit{J. Unterberger}, Ann. Probab. 37, No. 2, 565--614 (2009; Zbl 1172.60007) Full Text: DOI arXiv
Hu, Yaozhong; Nualart, David Rough path analysis via fractional calculus. (English) Zbl 1175.60061 Trans. Am. Math. Soc. 361, No. 5, 2689-2718 (2009). Reviewer: Maria Stolarczyk (Katowice) MSC: 60L20 60H10 60H05 26A42 26A33 46E35 PDF BibTeX XML Cite \textit{Y. Hu} and \textit{D. Nualart}, Trans. Am. Math. Soc. 361, No. 5, 2689--2718 (2009; Zbl 1175.60061) Full Text: DOI arXiv
Lejay, Antoine Stochastic differential equations driven by processes generated by divergence form operators. II: Convergence results. (English) Zbl 1185.60061 ESAIM, Probab. Stat. 12, 387-411 (2008). MSC: 60H10 60J60 PDF BibTeX XML Cite \textit{A. Lejay}, ESAIM, Probab. Stat. 12, 387--411 (2008; Zbl 1185.60061) Full Text: DOI EuDML
Picard, Jean A tree approach to \(p\)-variation and to integration. (English) Zbl 1157.60055 Ann. Probab. 36, No. 6, 2235-2279 (2008). Reviewer: A. A. Dorogovtsev (Kyïv) MSC: 60H05 26A42 60G17 PDF BibTeX XML Cite \textit{J. Picard}, Ann. Probab. 36, No. 6, 2235--2279 (2008; Zbl 1157.60055) Full Text: DOI arXiv
Feng, Chunrong; Zhao, Huaizhong Rough path integral of local time. (English) Zbl 1172.60015 C. R., Math., Acad. Sci. Paris 346, No. 7-8, 431-434 (2008). Reviewer: Eckhard Platen (Broadway) MSC: 60H05 60H07 60H10 PDF BibTeX XML Cite \textit{C. Feng} and \textit{H. Zhao}, C. R., Math., Acad. Sci. Paris 346, No. 7--8, 431--434 (2008; Zbl 1172.60015) Full Text: DOI
Lyons, Terry; Victoir, Nicolas An extension theorem to rough paths. (English) Zbl 1134.60047 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 24, No. 5, 835-847 (2007). Reviewer: Henri Schurz (Carbondale) MSC: 60H99 34F05 34G99 46N30 60G17 93C99 PDF BibTeX XML Cite \textit{T. Lyons} and \textit{N. Victoir}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 24, No. 5, 835--847 (2007; Zbl 1134.60047) Full Text: DOI Numdam EuDML
Quer-Sardanyons, Lluís; Tindel, Samy The 1-d stochastic wave equation driven by a fractional Brownian sheet. (English) Zbl 1123.60049 Stochastic Processes Appl. 117, No. 10, 1448-1472 (2007). MSC: 60H15 60G15 35L05 PDF BibTeX XML Cite \textit{L. Quer-Sardanyons} and \textit{S. Tindel}, Stochastic Processes Appl. 117, No. 10, 1448--1472 (2007; Zbl 1123.60049) Full Text: DOI arXiv HAL
Coutin, Laure; Friz, Peter; Victoir, Nicolas Good rough path sequences and applications to anticipating stochastic calculus. (English) Zbl 1132.60053 Ann. Probab. 35, No. 3, 1172-1193 (2007). Reviewer: Michael Högele (Berlin) MSC: 60H99 60H10 PDF BibTeX XML Cite \textit{L. Coutin} et al., Ann. Probab. 35, No. 3, 1172--1193 (2007; Zbl 1132.60053) Full Text: DOI arXiv
Lejay, Antoine Stochastic differential equations driven by processes generated by divergence form operators. I: A Wong-Zakai theorem. (English) Zbl 1181.60085 ESAIM, Probab. Stat. 10, 356-379 (2006). MSC: 60H10 60J60 PDF BibTeX XML Cite \textit{A. Lejay}, ESAIM, Probab. Stat. 10, 356--379 (2006; Zbl 1181.60085) Full Text: DOI Numdam EuDML
Gubinelli, Massimiliano; Lejay, Antoine; Tindel, Samy Young integrals and SPDEs. (English) Zbl 1103.60062 Potential Anal. 25, No. 4, 307-326 (2006). MSC: 60H15 60H05 PDF BibTeX XML Cite \textit{M. Gubinelli} et al., Potential Anal. 25, No. 4, 307--326 (2006; Zbl 1103.60062) Full Text: DOI arXiv
Friz, Peter; Victoir, Nicolas A note on the notion of geometric rough paths. (English) Zbl 1108.34052 Probab. Theory Relat. Fields 136, No. 3, 395-416 (2006). Reviewer: George Stoica (Saint John) MSC: 34F05 60G17 34A26 60H10 PDF BibTeX XML Cite \textit{P. Friz} and \textit{N. Victoir}, Probab. Theory Relat. Fields 136, No. 3, 395--416 (2006; Zbl 1108.34052) Full Text: DOI arXiv
Lejay, Antoine; Victoir, Nicolas On \((p,q)\)-rough paths. (English) Zbl 1097.60048 J. Differ. Equations 225, No. 1, 103-133 (2006). MSC: 60H10 34F05 PDF BibTeX XML Cite \textit{A. Lejay} and \textit{N. Victoir}, J. Differ. Equations 225, No. 1, 103--133 (2006; Zbl 1097.60048) Full Text: DOI
Lyons, Terry J.; Yam, Phillip S. C. On Gauss-Green theorem and boundaries of a class of Hölder domains. (English) Zbl 1103.28007 J. Math. Pures Appl. (9) 85, No. 1, 38-53 (2006). Reviewer: Vasile Ionescu (Bucureşti) MSC: 28A80 26B20 26B30 26B35 PDF BibTeX XML Cite \textit{T. J. Lyons} and \textit{P. S. C. Yam}, J. Math. Pures Appl. (9) 85, No. 1, 38--53 (2006; Zbl 1103.28007) Full Text: DOI
Marty, Renaud Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations. (English) Zbl 1136.60317 ESAIM, Probab. Stat. 9, 165-184 (2005). MSC: 60F05 34A45 34F05 60G15 60H10 PDF BibTeX XML Cite \textit{R. Marty}, ESAIM, Probab. Stat. 9, 165--184 (2005; Zbl 1136.60317) Full Text: DOI Numdam EuDML
Marty, Renaud Limit theorem for a differential equation with a long-range random coefficient. (Théorème limite pour une équation différentielle à coefficient aléatoire à mémoire longue.) (French) Zbl 1038.60033 C. R., Math., Acad. Sci. Paris 338, No. 2, 167-170 (2004). Reviewer: Dominique Lepingle (Orléans) MSC: 60G15 60H10 PDF BibTeX XML Cite \textit{R. Marty}, C. R., Math., Acad. Sci. Paris 338, No. 2, 167--170 (2004; Zbl 1038.60033) Full Text: DOI