Born: January 21, 1939 in Gomel, Belorussia, USSR.
Education:1956-1961: M.Sc. in Mathematics, Department of Mechanics and Mathematics, Moscow State University, USSR
1963-1966: Post-graduate course in probability theory and mathematical statistics, Department of Mechanics and Mathematics, Moscow State University, USSR
1974: Ph. D. in Physical and Mathematical Sciences, Institute of Mathematics, USSR Academy of Sciences, Leningrad
1975: Doctor of Sciences in Physical and Mathematical Sciences, Institute of Physics of the Earth, USSR Academy of Sciences, Moscow
Professional Career:
1966-1974: Researcher, Institute of Physics of the Earth, USSR Academy of Sciences, Moscow
1975-1989: Senior Researcher Fellow, O.Ju.Shmidt Institute of the Physics of the Earth, Ac. Sci. USSR
1995-2003: Visiting Researcher , Observatoire de Nice, France
1992-2004: Co-Editor of Computational Seismology journal
1990-2000: Leading Researcher, International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow
1993-2007: Visiting Researcher, the Abdus Salam International Center for Theoretical Physics, Trieste Italy (SAND group)
2002-2007: Staff Associate , the Abdus Salam International Center for Theoretical Physics, Trieste Italy (SAND group)
Areas of interest:
Stochastic processes, mathematical statistics, multifractal analysis, seismicity, earthquake prediction
Main Results:
Random processes.
- Characterisation of Gaussian random Fields with Markov property (the Levy and McKean problem ); Description of Levy fields on homogeneous spaces of rank 1 ( the Gangolly problem) and analysis of their Markov property;
- Exact resolution thresholds for close frequencies in spectral analysis of random processes; theoretical analysis of frequency resolution for practically interesting methods;
- Multifractal analysis of turbulent cascades and rehabilitation of the Log-Normal hypothesis of Kolmogorov;
- Fractional Brownian Motion (FBM) and one-sided exit problem: exact values of survival exponents for processes and fields of this type. A similar result for the integral FBM process confirmed the Sinai-Frisch hypothesis about the magnitude of the fractal dimension of singularities in solution of the viscosity-free Burgers equation with initial FBM data.
Seismisity.
- Seismic risk: statistical analysis of the feasibility of anti-seismic reinforcement of the Baikal-Amur railroud (pioneering work in economic and statistical analysis of seismic risk); applications of the developed methodology to the insurance and population risk in large cities ; multi-scale seismicity model and its applications to earthquake recurrence analysis;
- Macroseismics: visualization of isoseismic uncertainty to see the relationship between shaking geometry and earthquake source;
- Forecast: Theoretical analysis of earthquake prediction as a decision-making problem: description of optimal strategies in terms of errors diagrams;
- precursors: statistical analysis of earthquake precursors and forecasting methods ( M8, CSEP-methodology), evaluation of forecasting efficiency;
- seismicity laws: Theoretical and statistical analysis of scaling laws of seismicity: inter event time and fractality of hypocenters. Critical analysis of fractal methodology in risk problems;
- seismicity models: theoretical analysis of event clusters in epidemic-type seismicity models: event number distributions and Bath’s law. Confirmation of the cascade structure of aftershocks on this basis
Основные публикации
Molchan G.M., Gaussian stationary processes with asymptotic power spectrum. Soviet Math. Dokl., 1969, 10:1, 134-137.
Molchan G.M., Keilis-Borok V.I., Vilkovich Ye.V., Seismicity and principal seismic effects. Geophys. J. R., Astr. Soc., 1970, 21, 3-4, 323-335.
Molchan G.M., Characterization of Gaussian fields with markovian property. Soviet Math. Dokl., 1971, 12:2, 563-567.
Caputo M., Keilis-Borok V.I., Kronrod T.L., Molchan G.M., Panza G., Models of Earthquake occurrence and isoseimals in Italy. Annali di Geofisica, 1973, v.26, N2-3, 421-444.
Caputo M., Keilis-Borok V.I., Kronrod T.L., Molchan G.M., Panza G., Piva E., Podgaetskaya V.M., and Postpishl D., Seismic risk in Central Italy. Annali di Geofisica, 1974, N.1-2, 349-365.
Molchan G.M., L-Markov Gaussian field. Soviet Math. Dokl. 1974, 15:2, 657-662.
Molchan G.M., The Markov property of Levy fields on space of constant curvature. Soviet Math. Dokl., 1975, 16:2, 528-532.
Molchan G.M., On homogeneous random fields on symmetric space of rank 1, Theor. Probab. and Math. Statist., 1980, N21, 143-168.
Molchan G.M., Kronrod T.L., Calculation of seismic risk. In: Bune V.I.,Gorshkov G.P. (eds) Seismic Zoning of the Territory of the USSR, Moskow, Nauka, 1980, 69-82.
Keilis-Borok V.I., Molchan G.M., Gotsadze O.D., Koridze A.Kh., Kronrod T.L., An insurance-oriented pilot estimation of seismic risk for rural dwellings in Georgia. The Geneva Papers on Risk and Insurance, 1984, Etudes et Dossiers 77: 85-111, Natural Disasters and Insurance (IV).
Molchan G.M., Multiparameter Brownian motion. Theor. Probab. and Math. Statist, N36, 1988, 97-110, AMS.
Molchan G.M., Gaussian quasi-Markov processes with stationary increments. Theor. Probab. and Math. Statist, N37, 1988, 121-128, AMS.
Molchan G.M., Multiparametric Brownian motion on symmetric spaces. Probability Theory and Math. Stat. Proc. of the 4-th Vilnius Conference, Vol 2, ed. Prohorov Y.V. et al, VNUSCIENCE Press Utrecht, 1987, 275-286.
Molchan G.M., Strategies in strong earthquake prediction. Phys. Earth and Planet. Inter., 1990, 61, 1-2: 84-98.
Molchan G.M. and Dmitrieva O.E., Dynamics of the magnitude-frequency relation for foreshocks. Phys. Earth and Planet. Inter., 1990, 61, 1-2: 99-112.
Molchan G.M., Dmitrieva O.E., Rotwain I.M. and Dewey J., Statistical analysis of the results of earthquake prediction, based on bursts of aftershocks. Phys. Earth Planet. Inter., 1990, 61, 1-2: 128-138.
Molchan G.M., Exact resolution thresholds for close frequencies. Probability Theory and Math. Statistics: Proceedings of the 5-th Vilnius conference, 1990, Vol.2, (eds.) Grigelionis et al. MOKSLAS Vilnious. VSP-Utrecht, 193-206.
Molchan G.M., Structure of optimal strategies in earthquake prediction. Tectonophysics, 1991, 193: 267-276.
Molchan G.M. and Dmitrieva O.E., Aftershock identification: methods and new approaches. Geophys. J. Int., 1992, 109, 3: 501-516.
Molchan G.M. and O.E. Dmitrieva, Interaction of seismic events for short times and great distances. Doklady RAS1992, v.325-1, 56-59.
Molchan G.M. and Kagan Y., Earthquake prediction and its optimization. J. Geophys. Res., 1992, 97, N134, 4823-4838.
Molchan G.M., On feasibility of frequency resolution in spectral analysis. In D.K. Chowdhury (ed.), Computational Seismology and Geodynamics / Am. Geophys. Un., 1, Washington, D.C.: The Union, 1994: 95-107.
Molchan G.M. and Newman W.I., A theoretical analysis of the methods of harmonic decomposition. In D.K. Chowdhury (ed.), Computational Seismology and Geodynamics / Am. Geophys. Un., 1, Washington, D.C.: The Union, 1994: 108-117.
Molchan G.M., Frequency estimation performance by eigenvector method. In D.K. Chowdhury (ed.), Computational Seismology and Geodynamics / Am. Geophys. Un., 2, Washington, D.C.: The Union, 1994: 162-174.
Molchan G.M., Models for optimization of earthquake prediction. In D.K. Chowdhury (ed.), Computational Seismology and Geodynamics / Am. Geophys. Un., 2, Washington, D.C.: The Union, 1994: 1-10.
Molchan G.M., Multifractal analysis of Brownian zero Set. Journal of Statistical Physics, 1995, vol.79, N3/4: 701-730.
Molchan G.M., Scaling exponents and multifractal dimensions for independent random cascades. Commun. Math. Phys., 1996, vol.179, 681-702.
Molchan G.M., Earthquake Prediction as a decision-making Problem. Pure. appl. Geophys., 1996, vol.147, N1, 1-15.
Molchan G.M., Turbulent cascades: limitations and statistical test of the log-normal hypothesis. Phys. of Fluids, 1997, 9(8): 2387-2396.
Molchan G.M., Burgers equation with self-similar Gaussian initial data: tail probabilities. Journal of Statistical Physics, 1997, 88, 5/6: 1139-1150.
Molchan G.M., Earthquake Prediction as a Decision-making Problem. Pure. appl. Geophys., 1997, vol.149: 233-247.
Kronrod T.L. and Molchan G.M., Model of seismicity for the Caucasus Test Area. In D. Giardini and S. Balassanian (eds), Historical and Prehistirical Earthquakes in the Caucasus (Proceeding of the NATO ARW on Historical and Prehistirical Earthquakes in the Caucasus, Yerevan, Armenia, Jul 11-15, 1996). Kluwer Academic Publishers, 1997, ILP Publication, 333: 485-501.
Molchan G.M., Kronrod T.L. and Panza G.F., Multi-scale seismicity model for seismic risk. Bull. of the Seismological Society of America, 1997, vol.87, N5, 1220-1229.
Molchan G.M., Anomallies in multifractal formalism for local time of Brownian motion. Journal of Statistical Physics, 1998, vol.91, N1/2: 199-220.
Molchan G.M., On the maximum of a fractional Brownian motion. Theory of Prob. and its Applications, 2000, v.44:1, 97-102.
Molchan G.M., Maximum of fractional Brownian motion: probabilities of small values. Commun. Math. Phys., 1999, vol.205, N1,: 97-111.
Molchan G.M., Dmitrieva O.E., Kronrod T.L., Nekrasova A.K., Hazard-oriented multiscale seismicity model: Italy. In Chowdhury D.K. (ed.), Computational Seismology and Geodynamics / Am. Geophys. Un., 4, Washington, D.C.: The Union, 1999: 138-156.
Molchan G.M., Kronrod T.L., Nekrasova A.K., Immediate foreshocks: time variation of the b-value. Phys. of the Earth and Planet. Inter., 1999, vol.111, N3-4: 229-240.
Molchan G.M., On a maximum of stable Levy processes. Theory of Prob. and its Applications, 2001, v.45, 343-349.
Molchan G.M., Linear problems for fractional Brownian motion: group approach. Theory Probab. Appl., 2002, 47:1.
Molchan G.M., Turcotte D.L., A stochastic model of sedimentation: probabilities and multifractality. Euro. Jnl. Applied Math., 2002, vol.13, part 4, 371-383.
Molchan G.M., Historical comments to the fractional Brownian motion. In: Donkhan P., Oppenheim G., Taqqu M. (eds.) Long-range dependence: Theory and Applications, vol.1, 2002, Birkhauser Production, pp. 39-42.
Molchan G.M., Mandelbrot cascade measures independent of branching parameter. J. Stat. Phys., 2002, v.107:5-6, 977-988.
Molchan G.M., Kronrod T.L., Panza G., Shape analysis of isoseismals based on empirical and synthetic data. Pure and Appl. Geophys., 2002, vol.159, N6, 1229-1251.
Kronrod T.L., Molchan G.M., Panza G., Podgaetskaya V.M., Formalized representation of isoseismal uncertainty for Italian earthquakes. Bollettino di Geofisica Teorica ed Applicata (BGTA), 2002, v.41, N3-4, pp.243-313.
Molchan G.M., Earthquake prediction strategies: a theoretical analysis. Ch 5 (209-237) in the book: Keilis-Borok V.I. and Soloviev A.A. (eds), Nonlinear dynamics of the lithosphere and earthquake prediction. Springer. 2002, 335 pp.
Molchan G.M., On the uniqueness of the branching parameter for a random cascade measure , J. Stat. Phys. 2004, 115:3-4, 873-886.
Molchan G.M., Khokhlov A.V., Small values of the maximum for the integral of fractional Brownian motion , J. Stat. Phys. 2004, 114:3-4, 923-946.
Molchan G.M., Kronrod T.L., Panza G., Shape of empirical and synthetic isoseismals: comparison for Italian earthquakes of M < 6. Pure. appl. Geophys., 2004, vol.161, 1725-1747.
Molchan G.M., Interevent time distribution of seismicity: a theoretical approach, Pure. appl. Geophys., 2005, vol.162, 1135-1150.
Molchan G.M., Kronrod T.L., On the spatial scaling of seismicity rate, Geophys. J. Int. 2005, vol.162, 899-909..
Molchan G.M., Kronrod T.L., Seismic Interevent time: a spatial scaling and multifractality, Pure. appl. Geophys., 2007, 164, 75-96.
Molchan G.M., Unilateral small deviations of processes related to the fractional Brownian Motion, Stochastic processes and their applications, 2008,118:2085-2097.
Molchan G.M. and Keilis-Borok V.I., Earthquake Prediction: probabilistic aspect, . Geophys. J. International, 2008, 173, 3: 1012-1017.
Molchan G., Kronrod T., The fractal description of seismicity. Geophys. J. Int., 2009, 179, N3, 1787-1799.
Molchan G, Space-Time Earthquake Prediction: the Error Diagrams. Pure Appl. Geophys., 2010, 167, N8-9, 907-917, DOI: 10.1007/s00024-010-0087-z
Molchan G and L.Romashkova, Earthquake Prediction analysis based on empirical seismic rate: the M8 algorithm. Geophys. J. Int., 2010,183, 1525-1537.
Molchan G, T. Kronrod. Hot-Cold Spots in Italian Macroseismic Data. Pure Applied Geophysics, 2011,168,739-752, DOI: 10.1007/s00024-010-0111-3
Molchan G and L.Romashkova, Gambling Score in Earthquake Prediction Analysis. Geophys. J. Int., 2011,184,1445-1454
Molchan G, On the testing of seismicity models, Acta Geophysica, 2012, 60, DOI: 10.2478/s11600-0110042-0
Molchan G Stochastic earthquake source model: the omega-square hypothesis Geophys. J. Int. (2015) 202, 497–513
Molchan G, L. Romashkova and A. Peresan On some methods for assessing earthquake predictions Geophys. Int. (2017) 210, 1474–1480 DOI: 10.1093/gji/ggx23
Molchan G Survival exponents for fractional Brownian motion with multivariate time ALEA, Lat. Am. J. Probab. Math. Stat. 14, 1–7 , 2017.
Molchan G, The Inviscid Burgers Equation with Fractional Brownian Initial Data: The Dimension of Regular Lagrangian. J. Statistical Physics. 167,6, pp 1546–1554, 2017. DOI 10.1007/s10955-017-1791-1
Molchan G. Persistence Exponents for Gaussian Random Fields of Fractional Brownian Motion Type. J.Statistical Physics. 2018 DOI: 10.1007/s10955-018-2155-1
Molchan G, Leadership Exponent in the Pursuit Problem for 1-D Random Particles Statistical Physics (2020) 181:952–967 DOI: 10.1007/s10955-020-02614-z
Molchan ,. Fractal Seismicity and Seismic Risk, Izvestiya, Physics of the Solid Earth, 2020, Vol. 56, No. 1, pp. 66–73.
Molchan G, Gusev’s Stochastic Model for the Seismic Source: High-Frequency Behavior in the Far Zone Izvestiya, Physics of the Solid Earth, 2020, Vol. 56, No. 1, pp. 74–82.( In memoriam A.A. Gusev)
Molchan G, E. Varini and A. Peresan, Productivity within the epidemic-type seismicity model Geophys. J. Int. (2022) 231, 1545–1557 DOI: 10.1093/gji/ggac269
Molchan G , Persistence Exponents of Gaussian Random Fields Connected by the Lamperti Transform . J. Statistical Physics (2022) 186:21 DOI: 10.1007/s10955-021-02864-5
Molchan G. and E. Varini . The strongest aftershock in seismic models of epidemic type Geophys. J. Int. (2024) 236, 1440–1454 DOI: 10.1093/gji/ggae001. (In memoriam I. Zaliapin)
Molchan G. , Peresan A., Number of Aftershocks in Epidemic-type Seismicity Models . Geophys. J. Int. (2024) 239, 314–328. DOI: 10.1093/gji/ggae261