Molchan, G. The persistence exponents of Gaussian random fields connected by the Lamperti transform. (English) Zbl 1490.60081 J. Stat. Phys. 186, No. 2, Paper No. 21, 13 p. (2022). MSC: 60G15 60G22 60G60 PDFBibTeX XMLCite \textit{G. Molchan}, J. Stat. Phys. 186, No. 2, Paper No. 21, 13 p. (2022; Zbl 1490.60081) Full Text: DOI arXiv
Molchan, G. Leadership exponent in the pursuit problem for 1-D random particles. (English) Zbl 1466.60074 J. Stat. Phys. 181, No. 3, 952-967 (2020). MSC: 60G15 60G10 60G18 PDFBibTeX XMLCite \textit{G. Molchan}, J. Stat. Phys. 181, No. 3, 952--967 (2020; Zbl 1466.60074) Full Text: DOI arXiv
Molchan, G. Persistence exponents for Gaussian random fields of fractional Brownian motion type. (English) Zbl 1403.60031 J. Stat. Phys. 173, No. 6, 1587-1597 (2018). MSC: 60G15 60G22 60G60 PDFBibTeX XMLCite \textit{G. Molchan}, J. Stat. Phys. 173, No. 6, 1587--1597 (2018; Zbl 1403.60031) Full Text: DOI
Molchan, G. Integrated fractional Brownian motion: persistence probabilities and their estimates. arXiv:1806.04949 Preprint, arXiv:1806.04949 [math.PR] (2018). BibTeX Cite \textit{G. Molchan}, ``Integrated fractional Brownian motion: persistence probabilities and their estimates'', Preprint, arXiv:1806.04949 [math.PR] (2018) Full Text: arXiv OA License
Molchan, G. Factional Brownian motion with multivariate time in a large convex area: persistence exponents. arXiv:1803.01702 Preprint, arXiv:1803.01702 [math.PR] (2018). BibTeX Cite \textit{G. Molchan}, ``Factional Brownian motion with multivariate time in a large convex area: persistence exponents'', Preprint, arXiv:1803.01702 [math.PR] (2018) Full Text: arXiv OA License
Molchan, G. The inviscid Burgers equation with fractional Brownian initial data: the dimension of regular Lagrangian points. (English) Zbl 1375.35455 J. Stat. Phys. 167, No. 6, 1546-1554 (2017). MSC: 35Q53 60G22 PDFBibTeX XMLCite \textit{G. Molchan}, J. Stat. Phys. 167, No. 6, 1546--1554 (2017; Zbl 1375.35455) Full Text: DOI arXiv
Molchan, George Survival exponents for fractional Brownian motion with multivariate time. (English) Zbl 1355.60053 ALEA, Lat. Am. J. Probab. Math. Stat. 14, No. 1, 1-7 (2017). MSC: 60G22 PDFBibTeX XMLCite \textit{G. Molchan}, ALEA, Lat. Am. J. Probab. Math. Stat. 14, No. 1, 1--7 (2017; Zbl 1355.60053) Full Text: arXiv Link
Molchan, G. Survival exponents for some Gaussian processes. (English) Zbl 1260.60073 Int. J. Stoch. Anal. 2012, Article ID 137271, 20 p. (2012). MSC: 60G18 60G15 60G22 PDFBibTeX XMLCite \textit{G. Molchan}, Int. J. Stoch. Anal. 2012, Article ID 137271, 20 p. (2012; Zbl 1260.60073) Full Text: DOI arXiv
Molchan, G. Unilateral small deviations of processes related to the fractional Brownian motion. (English) Zbl 1151.60017 Stochastic Processes Appl. 118, No. 11, 2085-2097 (2008). MSC: 60G15 60G18 PDFBibTeX XMLCite \textit{G. Molchan}, Stochastic Processes Appl. 118, No. 11, 2085--2097 (2008; Zbl 1151.60017) Full Text: DOI
Molchan, G. The Problem of Small Unilateral Deviations: the Existence of Decay Exponents. arXiv:math/0608630 Preprint, arXiv:math/0608630 [math.PR] (2006). BibTeX Cite \textit{G. Molchan}, ``The Problem of Small Unilateral Deviations: the Existence of Decay Exponents'', Preprint, arXiv:math/0608630 [math.PR] (2006) Full Text: arXiv
Molchan, G.; Khokhlov, A. Small values of the maximum for the integral of fractional Brownian motion. (English) Zbl 1061.60037 J. Stat. Phys. 114, No. 3-4, 923-946 (2004). MSC: 60G15 28A80 82B41 82C41 PDFBibTeX XMLCite \textit{G. Molchan} and \textit{A. Khokhlov}, J. Stat. Phys. 114, No. 3--4, 923--946 (2004; Zbl 1061.60037) Full Text: DOI arXiv
Molchan, G. On the uniqueness of the branching parameter for a random cascade measure. (English) Zbl 1071.82024 J. Stat. Phys. 115, No. 3-4, 855-868 (2004). Reviewer: Messoud A. Efendiev (Berlin) MSC: 82B26 82B30 PDFBibTeX XMLCite \textit{G. Molchan}, J. Stat. Phys. 115, No. 3--4, 855--868 (2004; Zbl 1071.82024) Full Text: DOI arXiv
Molchan, George M. Historical comments related to fractional Brownian motion. (English) Zbl 1032.60035 Doukhan, Paul (ed.) et al., Theory and applications of long-range dependence. Boston, MA: Birkhäuser. 39-42 (2003). MSC: 60G15 60G25 60G18 PDFBibTeX XMLCite \textit{G. M. Molchan}, in: Theory and applications of long-range dependence. Boston, MA: Birkhäuser. 39--42 (2003; Zbl 1032.60035)
Molchan, G.; Khokhlov, A. Unilateral Small Deviations for the Integral of Fractional Brownian Motion. arXiv:math/0310413 Preprint, arXiv:math/0310413 [math.PR] (2003). MSC: 60G15 60G18 BibTeX Cite \textit{G. Molchan} and \textit{A. Khokhlov}, ``Unilateral Small Deviations for the Integral of Fractional Brownian Motion'', Preprint, arXiv:math/0310413 [math.PR] (2003) Full Text: arXiv
Molchan, G. M. Linear problems for a fractional Brownian motion: Group approach. (English. Russian original) Zbl 1035.60084 Theory Probab. Appl. 47, No. 1, 69-78 (2002); translation from Teor. Veroyatn. Primen. 47, No. 1, 59-70 (2002). Reviewer: Nicko G. Gamkrelidze (Moskva) MSC: 60J65 60G15 PDFBibTeX XMLCite \textit{G. M. Molchan}, Theory Probab. Appl. 47, No. 1, 69--78 (2002; Zbl 1035.60084); translation from Teor. Veroyatn. Primen. 47, No. 1, 59--70 (2002) Full Text: DOI
Molchan, G. M.; Turcotte, D. L. A stochastic model of sedimentation: probabilities and multifractality. (English) Zbl 1090.86006 Eur. J. Appl. Math. 13, No. 4, 371-383 (2002). MSC: 86A60 28A80 60G15 76M35 76T20 PDFBibTeX XMLCite \textit{G. M. Molchan} and \textit{D. L. Turcotte}, Eur. J. Appl. Math. 13, No. 4, 371--383 (2002; Zbl 1090.86006) Full Text: DOI
Molchan, G. Mandelbrot cascade measures independent of branching parameter. (English) Zbl 1016.76040 J. Stat. Phys. 107, No. 5-6, 977-988 (2002). MSC: 76F20 37N10 PDFBibTeX XMLCite \textit{G. Molchan}, J. Stat. Phys. 107, No. 5--6, 977--988 (2002; Zbl 1016.76040) Full Text: DOI
Molchan, G. M. On a maximum of stable Lévy processes. (English. Russian original) Zbl 1027.60042 Theory Probab. Appl. 45, No. 2, 343-349 (2000); translation from Teor. Veroyatn. Primen. 45, No. 2, 380-386 (2000). Reviewer: Vladimir Vatutin (Moskva) MSC: 60G51 60G52 60J70 PDFBibTeX XMLCite \textit{G. M. Molchan}, Theory Probab. Appl. 45, No. 2, 343--349 (2000; Zbl 1027.60042); translation from Teor. Veroyatn. Primen. 45, No. 2, 380--386 (2000) Full Text: DOI
Molchan, G. M. On the maximum of a fractional Brownian motion. (English. Russian original) Zbl 0966.60036 Theory Probab. Appl. 44, No. 1, 97-102 (1999); translation from Teor. Veroyatn. Primen. 44, No. 1, 111-115 (1999). Reviewer: Alexander V.Bulinskij (Moskva) MSC: 60G15 60G18 60G70 PDFBibTeX XMLCite \textit{G. M. Molchan}, Theory Probab. Appl. 44, No. 1, 97--102 (1999; Zbl 0966.60036); translation from Teor. Veroyatn. Primen. 44, No. 1, 111--115 (1999) Full Text: DOI
Molchan, G. M. Maximum of a fractional Brownian motion: Probabilities of small values. (English) Zbl 0942.60065 Commun. Math. Phys. 205, No. 1, 97-111 (1999). Reviewer: I.C.Vladimirescu (Craiova) MSC: 60J65 PDFBibTeX XMLCite \textit{G. M. Molchan}, Commun. Math. Phys. 205, No. 1, 97--111 (1999; Zbl 0942.60065) Full Text: DOI
Molchan, G. M. Anomalies in multifractal formalism for local time of Brownian motion. (English) Zbl 0929.60065 J. Stat. Phys. 91, No. 1-2, 199-220 (1998). Reviewer: N.M.Zinchenko (Kyïv) MSC: 60J65 28A80 82C31 PDFBibTeX XMLCite \textit{G. M. Molchan}, J. Stat. Phys. 91, No. 1--2, 199--220 (1998; Zbl 0929.60065) Full Text: DOI
Molchan, G. M. Turbulent cascades: limitations and a statistical test of the lognormal hypothesis. (English) Zbl 1185.76771 Phys. Fluids 9, No. 8, 2387-2396 (1997). MSC: 76F99 76M35 PDFBibTeX XMLCite \textit{G. M. Molchan}, Phys. Fluids 9, No. 8, 2387--2396 (1997; Zbl 1185.76771) Full Text: DOI
Molchan, G. M. Burgers equation with self-similar Gaussian initial data: Tail probabilities. (English) Zbl 0944.60073 J. Stat. Phys. 88, No. 5-6, 1139-1150 (1997). Reviewer: A.D.Borisenko (Kyïv) MSC: 60H15 PDFBibTeX XMLCite \textit{G. M. Molchan}, J. Stat. Phys. 88, No. 5--6, 1139--1150 (1997; Zbl 0944.60073) Full Text: DOI
Molchan, G. M. Scaling exponents and multifractal dimensions for independent random cascades. (English) Zbl 0853.76032 Commun. Math. Phys. 179, No. 3, 681-702 (1996). MSC: 76F20 76M35 37N99 PDFBibTeX XMLCite \textit{G. M. Molchan}, Commun. Math. Phys. 179, No. 3, 681--702 (1996; Zbl 0853.76032) Full Text: DOI
Molchan, G. M. Multifractal analysis of Brownian zero set. (English) Zbl 1081.60547 J. Stat. Phys. 79, No. 3-4, 701-730 (1995). MSC: 60J65 82B41 PDFBibTeX XMLCite \textit{G. M. Molchan}, J. Stat. Phys. 79, No. 3--4, 701--730 (1995; Zbl 1081.60547) Full Text: DOI
Molchan, G. M. Multi-monofractal properties of zeros of Brownian motion. (English. Russian original) Zbl 0836.60007 Russ. Acad. Sci., Dokl., Math. 49, No. 2, 350-354 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 335, No. 4, 424-426 (1994). Reviewer: Gong Guanglu (Beijing) MSC: 60D05 60J65 28A80 PDFBibTeX XMLCite \textit{G. M. Molchan}, Russ. Acad. Sci., Dokl., Math. 49, No. 2, 424--426 (1994; Zbl 0836.60007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 335, No. 4, 424--426 (1994)
Molchan, G. M. Exact resolution thresholds for close frequencies. (English) Zbl 0728.62093 Probability theory and mathematical statistics, Proc. 5th Vilnius Conf., Vilnius/Lith. 1989, Vol. II, 193-206 (1990). Reviewer: J.Anděl (Praha) MSC: 62M15 60G12 PDFBibTeX XML
Molchan, G. M. Gaussian quasi-Markov processes with stationary increments. (English. Russian original) Zbl 0663.60035 Theory Probab. Math. Stat. 37, 121-128 (1988); translation from Teor. Veroyatn. Mat. Stat., Kiev 37, 105-111 (1987). MSC: 60G15 60J27 PDFBibTeX XMLCite \textit{G. M. Molchan}, Theory Probab. Math. Stat. 37, 121--128 (1988; Zbl 0663.60035); translation from Teor. Veroyatn. Mat. Stat., Kiev 37, 105--111 (1987)
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 PDFBibTeX XMLCite \textit{G. M. Molchan}, Theory Probab. Math. Stat. 36, 97--110 (1988; Zbl 0659.60073); translation from Teor. Veroyatn. Mat. Stat. 36, 88--101 (1987)
Molchan, G. M. Multiparametric Brownian motion on symmetric spaces. (English) Zbl 0653.58045 Probability theory and mathematical statistics, Proc. 4th Conf., Vilnius/USSR 1985, Vol. 2, 275-286 (1987). Reviewer: F.Rouvière MSC: 58J65 60J65 PDFBibTeX XML
Molchan, G. M. Gaussian quasi-Markov processes with stationary increments. (Russian) Zbl 0646.60045 Teor. Veroyatn. Mat. Stat., Kiev 37, 105-111 (1987). Reviewer: A.Plikusas MSC: 60G15 60J27 PDFBibTeX XMLCite \textit{G. M. Molchan}, Teor. Veroyatn. Mat. Stat., Kiev 37, 105--111 (1987; Zbl 0646.60045)
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 PDFBibTeX XMLCite \textit{G. M. Molchan}, Teor. Veroyatn. Mat. Stat., Kiev 36, 88--101 (1987; Zbl 0637.60062)
Molchan, G. M. Stability in the problem of linear prediction of stationary processes. (English) Zbl 0528.62080 Sov. Math. 26, No. 1, 48-60 (1982). MSC: 62M20 60G25 60G10 PDFBibTeX XMLCite \textit{G. M. Molchan}, Sov. Math. 26, No. 1, 48--60 (1982; Zbl 0528.62080)
Molchan, G. M. Stability in a problem of linear prediction of stationary processes. (Russian) Zbl 0502.62082 Izv. Vyssh. Uchebn. Zaved., Mat. 1982, No. 1(236), 42-52 (1982). MSC: 62M20 60G25 60G10 PDFBibTeX XMLCite \textit{G. M. Molchan}, Izv. Vyssh. Uchebn. Zaved., Mat. 1982, No. 1(236), 42--52 (1982; Zbl 0502.62082)
Molchan, G. M. On homogeneous random fields on symmetric spaces of rank 1. (English) Zbl 0485.60054 Theory Probab. Math. Stat. 21, 143-168 (1980). MSC: 60G60 60B99 33C45 32M15 PDFBibTeX XMLCite \textit{G. M. Molchan}, Theory Probab. Math. Stat. 21, 143--168 (1980; Zbl 0485.60054)
Molchan, G. M. On homogeneous random fields on symmetric spaces of rank one. (Russian) Zbl 0412.60057 Teor. Veroyatn. Mat. Stat. 21, 123-148 (1979). MSC: 60G60 42A99 PDFBibTeX XML
Molchan, G. M. The Markov property of Levy fields on spaces of constant curvature. (English. Russian original) Zbl 0335.60032 Sov. Math., Dokl. 16, 528-532 (1975); translation from Dokl. Akad. Nauk SSSR 221, 1276-1279 (1975). MSC: 60G20 60J25 51M10 PDFBibTeX XMLCite \textit{G. M. Molchan}, Sov. Math., Dokl. 16, 528--532 (1975; Zbl 0335.60032); translation from Dokl. Akad. Nauk SSSR 221, 1276--1279 (1975)
Molchan, G. M. L-Markov Gaussian fields. (English. Russian original) Zbl 0337.60041 Sov. Math., Dokl. 15, 657-662 (1974); translation from Dokl. Akad. Nauk SSSR 215, 1054-1057 (1974). MSC: 60G20 32A15 46C99 PDFBibTeX XMLCite \textit{G. M. Molchan}, Sov. Math., Dokl. 15, 657--662 (1974; Zbl 0337.60041); translation from Dokl. Akad. Nauk SSSR 215, 1054--1057 (1974)
Molchan, G. M. On some problems concerning Brownian motion in Levy’s sense. (English. Russian original) Zbl 0159.46504 Theor. Probab. Appl. 12, 682-690 (1967); translation from Teor. Veroyatn. Primen. 12, 747-755 (1967). PDFBibTeX XMLCite \textit{G. M. Molchan}, Theory Probab. Appl. 12, 682--690 (1967; Zbl 0159.46504); translation from Teor. Veroyatn. Primen. 12, 747--755 (1967) Full Text: DOI