Kurchenko, O. O.; Syniavska, O. O. Consistent estimates of the parameters of the multiparameter fractional Brownian motion. (English) Zbl 1538.60059 Theory Stoch. Process. 27, No. 1, 31-40 (2023). MSC: 60G22 60G15 62F12 × Cite Format Result Cite Review PDF Full Text: Link
Tudor, Ciprian A. Fractional stochastic heat equation with Hermite noise. (English) Zbl 1515.60170 Grad. J. Math. 7, No. 2, 1-18 (2022). MSC: 60H05 60H15 60G22 × Cite Format Result Cite Review PDF Full Text: Link
Slaoui, Meryem; Tudor, C. A. The linear stochastic heat equation with Hermite noise. (English) Zbl 1436.60054 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 22, No. 3, Article ID 1950022, 23 p. (2019). MSC: 60H05 60H15 60G22 × Cite Format Result Cite Review PDF Full Text: DOI
Araya, Héctor; Tudor, Ciprian A. Behavior of the Hermite sheet with respect to the Hurst index. (English) Zbl 1451.60052 Stochastic Processes Appl. 129, No. 7, 2582-2605 (2019). Reviewer: Nicolas Privault (Singapore) MSC: 60H07 60G22 × Cite Format Result Cite Review PDF Full Text: DOI
Sottinen, Tommi; Viitasaari, Lauri Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions. (English) Zbl 1352.60056 Mod. Stoch., Theory Appl. 2, No. 3, 287-295 (2015). MSC: 60G15 60G60 60H05 60J65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Richard, Alexandre A fractional Brownian field indexed by \(L^2\) and a varying Hurst parameter. (English) Zbl 1319.60111 Stochastic Processes Appl. 125, No. 4, 1394-1425 (2015). MSC: 60G60 60G22 60G15 60G51 60G17 28C20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Herbin, Erick; Arras, Benjamin; Barruel, Geoffroy From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields. (English) Zbl 1312.60065 ESAIM, Probab. Stat. 18, 418-440 (2014). MSC: 60G60 60G15 60G17 60G10 60G22 28A78 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Malyarenko, Anatoliy A family of series representations of the multiparameter fractional Brownian motion. (English) Zbl 1247.60052 Dalang, Robert C. (ed.) et al., Seminar on stochastic analysis, random fields and applications VI. Centro Stefano Franscini, Ascona, Italy, May 19–23, 2008. Basel: Birkhäuser (ISBN 978-3-0348-0020-4/pbk; 978-3-0348-0021-1/ebook). Progress in Probability 63, 209-226 (2011). MSC: 60G22 33C60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Jacka, Saul; Warren, Jon; Windridge, Peter Minimizing the time to a decision. (English) Zbl 1230.93100 Ann. Appl. Probab. 21, No. 5, 1795-1826 (2011). MSC: 93E20 60J70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Zikun Some topics in the mathematical theory of Brownian motion. (Chinese. English summary) Zbl 1240.60226 Acta Math. Sci., Ser. A, Chin. Ed. 30, No. 5, 1242-1247 (2010). MSC: 60J65 × Cite Format Result Cite Review PDF
Chen, Zhenlong Multiparameter generalized Brownian sheet images and capacity. (Chinese. English summary) Zbl 1199.60113 Acta Math. Sin., Chin. Ser. 52, No. 2, 269-280 (2009). MSC: 60G10 × Cite Format Result Cite Review PDF
Herbin, Erick; Lévy-Véhel, Jacques Stochastic 2-microlocal analysis. (English) Zbl 1175.60032 Stochastic Processes Appl. 119, No. 7, 2277-2311 (2009). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60G05 60G15 60G17 60G18 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Amirdjanova, Anna; Linn, Matthew Stochastic evolution equations for nonlinear filtering of random fields in the presence of fractional Brownian sheet observation noise. (English) Zbl 1145.60024 Comput. Math. Appl. 55, No. 8, 1766-1784 (2008). Reviewer: Vjatscheslav Vasiliev (Tomsk) MSC: 60G35 60G60 62M20 93E11 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pemantle, Robin; Peres, Yuval What is the probability of intersecting the set of Brownian double points? (English) Zbl 1131.60071 Ann. Probab. 35, No. 6, 2044-2062 (2007). Reviewer: Mohamed Hmissi (Tunis) MSC: 60J45 31A15 60J65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Sei, Tomonari Local asymptotic mixed normality of transformed Gaussian models for random fields. (English) Zbl 1107.62103 Stochastic Processes Appl. 117, No. 3, 375-398 (2007). MSC: 62M40 × Cite Format Result Cite Review PDF Full Text: DOI
Malyarenko, Anatoliy Functional limit theorems for multiparameter fractional Brownian motion. (English) Zbl 1120.60029 J. Theor. Probab. 19, No. 2, 263-288 (2006). Reviewer: Tadeusz Inglot (Wrocław) MSC: 60F17 60G60 60G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Anastassiou, George A.; Goldstein, Giséle Ruiz; Goldstein, Jerome A. Uniqueness for evolution in multidimensional time. (English) Zbl 1079.35032 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 64, No. 1, 33-41 (2006). MSC: 35G20 35A05 × Cite Format Result Cite Review PDF Full Text: DOI
Dozzi, Marco Occupation density and sample path properties of \(N\)-parameter processes. (English) Zbl 1042.60031 Merzbach, Ely (ed.), Topics in spatial stochastic processes. Lectures given at the C.I.M.E. summer school, Martina Franca, Italy, July 1–8, 2001. Berlin: Springer (ISBN 3-540-00295-2/pbk). Lect. Notes Math. 1802, 127-166 (2003). Reviewer: Peter Mörters (Bath) MSC: 60G60 60G17 60J55 × Cite Format Result Cite Review PDF
Khoshnevisan, Davar Multiparameter processes. An introduction to random fields. (English) Zbl 1005.60005 Springer Monographs in Mathematics. New York, NY: Springer. xix, 584 p. (2002). Reviewer: Yu.S.Mishura (Kyïv) MSC: 60-02 60G60 60G15 60G44 60F17 60G50 60J25 60J45 60J65 × Cite Format Result Cite Review PDF Full Text: DOI Backlinks: MO
Hu, Yaozhong; Øksendal, Bernt; Zhang, Tusheng Stochastic fractional potential theory. (English) Zbl 1020.31003 Heinonen, J. (ed.) et al., Papers on analysis: a volume dedicated to Olli Martio on the occasion of his 60th birthday. Jyväskylä: Univ. Jyväskylä, Institut für Mathematik und Statistik. Ber., Univ. Jyväskylä. 83, 169-180 (2001). Reviewer: Volker Metz (Bielefeld) MSC: 31C45 60H05 60G15 35R60 60H40 × Cite Format Result Cite Review PDF
Kurchenko, O. O. The convergence of a sequence of random fields in the space \(D([0,1]^d)\). (English. Ukrainian original) Zbl 0998.60029 Theory Probab. Math. Stat. 64, 93-103 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 82-91 (2001). Reviewer: N.M.Zinchenko (Kyïv) MSC: 60F17 60G60 × Cite Format Result Cite Review PDF
Øksendal, Bernt; Zhang, Tusheng Multiparameter fractional Brownian motion and quasi-linear stochastic partial differential equations. (English) Zbl 0986.60056 Stochastics Stochastics Rep. 71, No. 3-4, 141-163 (2001). Reviewer: E.Buckwar (Berlin) MSC: 60H15 60G15 60G18 35R60 × Cite Format Result Cite Review PDF Full Text: DOI Link
Lin, Zheng-Yan; Choi, Yong-Kab; Hwang, Kyo-Shin Some limit theorems on the increments of a multi-parameter fractional Brownian motion. (English) Zbl 0990.60025 Stochastic Anal. Appl. 19, No. 4, 499-517 (2001). Reviewer: Josef Steinebach (Marburg) MSC: 60F15 60G15 × Cite Format Result Cite Review PDF Full Text: DOI
Hu, Yaozhong; Øksendal, Bernt; Zhang, Tusheng Stochastic partial differential equations driven by multiparameter fractional white noise. (English) Zbl 0982.60054 Gesztesy, Fritz (ed.) et al., Stochastic processes, physics and geometry: New interplays. II. A volume in honor of Sergio Albeverio. Proceedings of the conference on infinite dimensional (stochastic) analysis and quantum physics, Leipzig, Germany, January 18-22, 1999. Providence, RI: American Mathematical Society (AMS). CMS Conf. Proc. 29, 327-337 (2000). Reviewer: Dirk Blömker (Augsburg) MSC: 60H15 35R60 60G60 60H05 × Cite Format Result Cite Review PDF
Kallianpur, G.; Papanicolaou, V. G. Exact computation of Feynman-type integrals involving Gaussian random fields. (English) Zbl 0962.60039 Stoch. Environ. Res. Risk Assess. 14, No. 1, 33-49 (2000). Reviewer: Vigirdas Mackevičius (Vilnius) MSC: 60G60 81S40 65C50 28C20 81Q30 × Cite Format Result Cite Review PDF Full Text: DOI
Kozachenko, Yuri V.; Kurchenko, Oleksandr O. An estimate for the multiparameter FBM. (English) Zbl 0992.62078 Theory Stoch. Process. 5(21), No. 3-4, 113-119 (1999). Reviewer: Mikhail Moklyachuk (Kyïv) MSC: 62M05 62M40 60G17 62F12 × Cite Format Result Cite Review PDF
Obata, Nobuaki A note on transformations on white noise functions. Hida’s whiskers revisited. (English) Zbl 0962.46033 RIMS Kokyuroku 1035, 155-169 (1998). Reviewer: V.Karunakaran (Madurai) MSC: 46F25 60G20 47A70 × Cite Format Result Cite Review PDF
Talagrand, Michel Multiple points of trajectories of multiparameter fractional Brownian motion. (English) Zbl 0928.60026 Probab. Theory Relat. Fields 112, No. 4, 545-563 (1998). Reviewer: Peter Mörters (Berlin) MSC: 60G15 60G17 60G18 28A78 × Cite Format Result Cite Review PDF Full Text: DOI
Delgado, Rosario; Jolis, Maria A Hu-Meyer formula for generalized multiple anticipating integrals. (English) Zbl 0947.60062 Stochastics Stochastics Rep. 58, No. 1-2, 115-138 (1996). Reviewer: M.Rao (Gainesville) MSC: 60H05 60H07 × Cite Format Result Cite Review PDF Full Text: DOI
N’Zi, Modeste On large deviation estimates for two parameter diffusion processes and applications. (English) Zbl 0831.60041 Stochastics Stochastics Rep. 50, No. 1-2, 65-83 (1994). MSC: 60F10 60H15 60J65 × Cite Format Result Cite Review PDF Full Text: DOI
Khmaladze, E. V. Goodness of fit problem and scanning innovation martingales. (English) Zbl 0801.62043 Ann. Stat. 21, No. 2, 798-829 (1993). Reviewer: E.Valkeila (Helsinki) MSC: 62G10 62F03 × Cite Format Result Cite Review PDF Full Text: DOI
Fatalov, V. R. Asymptotics of large deviation probabilities for Gaussian fields. (English. Russian original) Zbl 0815.60026 J. Contemp. Math. Anal., Armen. Acad. Sci. 27, No. 3, 48-70 (1992); translation from Izv. Akad. Nauk Armen., Mat. 27, No. 6, 59-85 (1992). MSC: 60F10 × Cite Format Result Cite Review PDF
Kojo, Katsuya; Takenaka, Shigeo On canonical representations of stable \(M_ t\)-processes. (English) Zbl 0788.60052 Probab. Math. Stat. 13, No. 2, 229-238 (1992). Reviewer: N.M.Zinchenko (Kiev) MSC: 60G18 60G07 60E07 60J65 60G60 × Cite Format Result Cite Review PDF
Zapała, A. M. Brownian sheets in a locally pseudoconvex metric linear space. (English) Zbl 0688.60066 Probability theory on vector spaces IV, Proc. Conf., Łańcut/Poland 1987, Lect. Notes Math. 1391, 406-424 (1989). Reviewer: A.M.Zapala MSC: 60J65 60B11 60G60 60G17 60F15 60B05 60G15 × Cite Format Result Cite Review PDF
Ossiander, Mina; Waymire, Edward C. Certain poitive-definite kernels. (English) Zbl 0677.60054 Proc. Am. Math. Soc. 107, No. 2, 487-492 (1989). Reviewer: P.Ressel MSC: 60G60 43A35 60G15 × Cite Format Result Cite Review PDF Full Text: DOI
Lacey, Michael T. A remark on the multiparameter law of the iterated logarithm. (English) Zbl 0677.60032 Stochastic Processes Appl. 32, No. 2, 355-367 (1989). Reviewer: B.L.S.Prakasa Rao MSC: 60F15 60G15 60G50 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Hong Lévy’s representation theorem of a certain class of stochastic processes under the increasing path. (Chinese. English summary) Zbl 0693.60040 J. Beijing Norm. Univ., Nat. Sci. 1988, No. 3, 1-6 (1988). MSC: 60G60 60G44 60J65 × Cite Format Result Cite Review PDF
Park, Chull; Skoug, David A note on Paley-Wiener-Zygmund stochastic integrals. (English) Zbl 0662.60063 Proc. Am. Math. Soc. 103, No. 2, 591-601 (1988). Reviewer: V.Mackevičius MSC: 60H05 60J65 60G60 × Cite Format Result Cite Review PDF Full Text: DOI
Molchan, G. M. Multiparameter Brownian motion. (English. Russian original) Zbl 0659.60073 Theory Probab. Math. Stat. 36, 97-110 (1988); translation from Teor. Veroyatn. Mat. Stat. 36, 88-101 (1987). MSC: 60G60 60J65 60G15 60J60 × Cite Format Result Cite Review PDF
Bass, Richard F. Probability estimates for multiparameter Brownian processes. (English) Zbl 0645.60044 Ann. Probab. 16, No. 1, 251-264 (1988). Reviewer: N.Leonenko MSC: 60G15 60F10 60G60 60G10 60J65 × Cite Format Result Cite Review PDF Full Text: DOI
Zapała, A. M. Brownian sheets with values in a Banach space. (English) Zbl 0698.60004 Ann. Univ. Mariae Curie-Skłodowska, Sect. A 41, 159-175 (1987). MSC: 60B05 46B20 60J65 × Cite Format Result Cite Review PDF
Bhattacharya, P. K. Maximum likelihood estimation of a change-point in the distribution of independent random variables: general multiparameter case. (English) Zbl 0659.62033 J. Multivariate Anal. 23, 183-208 (1987). Reviewer: R.Mentz MSC: 62F12 62H12 60F05 62E20 × Cite Format Result Cite Review PDF Full Text: DOI
Molchan, G. M. The multiparametric Brownian motion. (Russian) Zbl 0637.60062 Teor. Veroyatn. Mat. Stat., Kiev 36, 88-101 (1987). Reviewer: He Shengwu MSC: 60G60 60J65 60G15 60J60 × Cite Format Result Cite Review PDF
Lo, Albert Y. A remark on the limiting posterior distribution of the multiparameter Dirichlet process. (English) Zbl 0613.62016 Sankhyā, Ser. A 48, No. 1-2, 247-249 (1986). MSC: 62E20 62C10 62G99 60G99 × Cite Format Result Cite Review PDF
Walsh, John B. An introduction to stochastic partial differential equations. (English) Zbl 0608.60060 École d’été de probabilités de Saint-Flour XIV - 1984, Lect. Notes Math. 1180, 265-437 (1986). Reviewer: P.Kotelenez MSC: 60H15 60G60 × Cite Format Result Cite Review PDF
Tautu, Petre Random fields: Applications in cell biology. (English) Zbl 0605.60054 Stochastic spatial processes, Proc. Conf., Heidelberg/Ger. 1984, Lect. Notes Math. 1212, 258-299 (1986). Reviewer: K.Schürger MSC: 60G60 60K35 92F05 60J70 74A20 82B26 82B31 × Cite Format Result Cite Review PDF
Doss, H.; Dozzi, M. Estimations de grandes déviations pour les processus de diffusion a paramètre multidimensionnel. (Estimations of large deviations for diffusion processes with a multidimensional parameter). (French) Zbl 0604.60027 Probabilités XX, Proc. Sémin., Strasbourg 1984/85, Lect. Notes Math. 1204, 68-80 (1986). MSC: 60F10 60H20 60J60 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML
Tsujii, Yoshiki On modified Takagi functions of two variables. (English) Zbl 0609.26007 J. Math. Kyoto Univ. 25, 577-581 (1985). Reviewer: Wilfrid S.Kendall MSC: 26B35 26A27 28A75 60J65 × Cite Format Result Cite Review PDF Full Text: DOI
Gadzhiev, G. A. On a multitime equation and its reduction to a multiparameter spectral problem. (English. Russian original) Zbl 0605.35007 Sov. Math., Dokl. 32, 710-713 (1985); translation from Dokl. Akad. Nauk SSSR 285, 530-533 (1985). Reviewer: J.Weidmann MSC: 35F10 76D10 60J65 82D45 × Cite Format Result Cite Review PDF
Walsh, John B. Regularity properties of a stochastic partial differential equation. (English) Zbl 0567.60063 Stochastic processes, Semin. Gainesville/Fla. 1983, Prog. Probab. Stat. 7, 257-290 (1984). Reviewer: D.Kannan MSC: 60H15 60J70 60J65 × Cite Format Result Cite Review PDF
Csaki, E. On small values of the square integral of a multiparameter Wiener process. (English) Zbl 0536.60069 Statistics and probability, Proc. 3rd Pannonian Symp., Visegrád/Hung. 1982, 19-26 (1984). MSC: 60G60 60J65 × Cite Format Result Cite Review PDF
Zinchenko, N. M. On a functional law of iterated logarithm for a multiparameter Brownian motion. (Russian) Zbl 0577.60032 Teor. Veroyatn. Mat. Stat. 29, 46-51 (1983). Reviewer: C.Baldauf MSC: 60F17 60G60 60J65 × Cite Format Result Cite Review PDF
Dorea, Chang C. Y. A characterization of the multiparameter Wiener process and an application. (English) Zbl 0499.60049 Proc. Am. Math. Soc. 85, 267-271 (1982). MSC: 60G60 60F17 60J65 × Cite Format Result Cite Review PDF Full Text: DOI
Davydov, Yu. A. Strong convergence and local limit theorems for functionals of supremum type. (English) Zbl 0489.60008 J. Sov. Math. 20, 2143-2147 (1982). MSC: 60B10 60G60 60J65 × Cite Format Result Cite Review PDF Full Text: DOI
Nualart, D.; Sanz, M. A Markov property for two parameter Gaussian processes. (English) Zbl 0417.60084 Stochastica 3, No. 1, 1-16 (1979). MSC: 60J99 60G15 60J35 60H15 × Cite Format Result Cite Review PDF Full Text: EuDML
Davydov, Yu. A. La convergence forte et des theoremes locaux pour les repartitions des fonctionnelles du type de supremum. (Russian) Zbl 0417.60010 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 85, 39-45 (1979). MSC: 60B10 60J65 × Cite Format Result Cite Review PDF Full Text: EuDML
Walsh, John B. Convergence and regularity of multiparameter strong martingales. (English) Zbl 0395.60040 Z. Wahrscheinlichkeitstheor. Verw. Geb. 46, 177-192 (1979). MSC: 60G17 60G40 × Cite Format Result Cite Review PDF Full Text: DOI
Sanz Sole, Marta Stochastic differential calculus for processes with \(n\)-dimensional parameter. (Spanish) Zbl 0418.60058 Stochastica 2, No. 4, 51-70 (1978). MSC: 60H05 60H15 60J65 × Cite Format Result Cite Review PDF Full Text: EuDML
Wolpert, Robert L. Wiener path intersections and local time. (English) Zbl 0403.60069 J. Funct. Anal. 30, 329-340 (1978). MSC: 60J55 60J65 × Cite Format Result Cite Review PDF Full Text: DOI