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Michael Tretyakov

Deputy Head of School and Professor of Mathematics, Faculty of Science

Personal Details
Research
Publications

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workRoom C04 Mathematical Sciences
University Park
Nottingham
NG7 2RD
UK
work0115 9514954
Michael.Tretyakov@nottingham.ac.uk
https://www.maths.nottingham.ac.uk/plp/pmzmt/

Expertise Summary

Research Summary

Current Research interests: Numerical integration of stochastic differential equations, probabilistic approach to numerical solution of nonlinear partial differential equations, financial… read more

Selected Publications

G.N. MILSTEIN and M.V. TRETYAKOV, 2004. Stochastic Numerics for Mathematical Physics. Springer.
M.V. TRETYAKOV, 2013. Introductory Course on Financial Mathematics Imperial College Press.
BAYLISS, C. D., FALLAIZE, C., HOWITT, R. and TRETYAKOV, M. V., 2019. Mutation and Selection in Bacteria: Modelling and Calibration BULLETIN OF MATHEMATICAL BIOLOGY. 81(3), 639-675
IGLESIAS, MARCO, PARK, MINHO and TRETYAKOV, M., V, 2018. Bayesian inversion in resin transfer molding INVERSE PROBLEMS. 34(10),

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Current Research

Current Research interests: Numerical integration of stochastic differential equations, probabilistic approach to numerical solution of nonlinear partial differential equations, financial mathematics, uncertainty quantification, stochastic dynamics and modeling in genetics.

MILSTEIN G.N. and TRETYAKOV M.V., 2021. Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation Numerical Mathematics: Theory, Methods and Applications. 14(1), 1-30
BAILEY, N. Y., HIBBERD, S., POWER, H. and TRETYAKOV, M., V, 2019. Effect of Uncertainty in External Forcing on a Fluid Lubricated Bearing PROCEEDINGS OF THE 10TH INTERNATIONAL CONFERENCE ON ROTOR DYNAMICS - IFTOMM, VOL. 4. 63, 443-459
BAYLISS, C. D., FALLAIZE, C., HOWITT, R. and TRETYAKOV, M. V., 2019. Mutation and Selection in Bacteria: Modelling and Calibration BULLETIN OF MATHEMATICAL BIOLOGY. 81(3), 639-675
BAILEY N.Y, HIBBERD S., POWER H. and TRETYAKOV M.V., 2019. Effect of random forcing on fluid lubricated bearing IMA J. Appl. Math. 84(3), 632-649
M.Y. MATVEEV, F.G. BALL, I.A. JONES, A.C. LONG, P.J. SCHUBEL and M.V. TRETYAKOV, 2018. Uncertainty in geometry of fibre preforms manufactured with Automated Dry Fibre Placement and its effects on permeability Journal of Composite Materials. 52,
IGLESIAS, MARCO, PARK, MINHO and TRETYAKOV, M., V, 2018. Bayesian inversion in resin transfer molding INVERSE PROBLEMS. 34(10),
BAILEY, N. Y., HIBBERD, S., POWER, H. and TRETYAKOV, M. V., 2018. Evaluation of the minimum face clearance of a high-speed gas-lubricated bearing with Navier slip boundary conditions under random excitations JOURNAL OF ENGINEERING MATHEMATICS. 112(1), 17-35
M. PARK and M.V. TRETYAKOV, 2017. Stochastic resin transfer molding process SIAM/ASA Journal on Uncertainty Quantification. 5(1), 1110–1135
R. L. DAVIDCHACK, T. E. OULDRIDGE and M.V. TRETYAKOV, 2017. Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions J. Chem. Phys.. 147(22), 224103
G.N. MILSTEIN and M.V. TRETYAKOV, 2016. Layer methods for Navier-Stokes equations with additive noise using simplest characteristics J. Comp Appl. Maths.. 302, 1–23
Z. ZHANG, M.V. TRETYAKOV, B.L. ROZOVSKII and G. E. KARNIADAKIS, 2015. Wiener chaos vs stochastic collocation methods for linear advection-diffusion-reaction equations with multiplicative white noise SIAM J. Numer. Anal.. 53(1), 153-183
R. L. DAVIDCHACK, T. E. OULDRIDGE and M. V. TRETYAKOV, 2015. New Langevin and gradient thermostats for rigid body dynamics J. Chem. Phys.. 142(14), 144114
M. PARK and M.V. TRETYAKOV, 2015. A block circulant embedding method for simulation of stationary Gaussian random fields on block-regular grids Int. J. Uncertainty Quantification. 5(6), 527-544
M.V. TRETYAKOV, 2015. Stochastic filtering. In: BJORN ENGQUIST, ed., Encyclopedia of Applied and Computational Mathematics Springer.
M. KRIVKO and M.V. TRETYAKOV, 2014. Numerical integration of Heath-Jarrow-Morton model of interest rates IMA J. Numer. Anal.. 34, 147–196
Z. ZHANG, M.V. TRETYAKOV, B.L. ROZOVSKII and G. E. KARNIADAKIS, 2014. A recursive sparse grid collocation method for differential equations with white noise SIAM J. Sci. Comp.. 36(4), A1652-A1677
B. LEIMKUHLER, C. MATTHEWS and M.V. TRETYAKOV, 2014. On the long-time integration of stochastic gradient systems Proc. R. Soc. A. 470(2170), 20140120
G.N. MILSTEIN and M.V. TRETYAKOV, 2013. Layer methods for the incompressible Navier-Stokes equations with space periodic conditions Advances in Applied Probability. 45(3), 742-772
M. KRIVKO and M.V. TRETYAKOV, 2013. Application of simplest random walk algorithms for pricing barrier options. In: T. GERSTNER and P.E. KLOEDEN, eds., Recent Developments in Computational Finance World Scientific.
A. CANGIANI, R.L. DAVIDCHACK, E. GEORGOULIS, A.N. GORBAN, J. LEVESLEY and M.V. TRETYAKOV, eds., 2013. Numerical Mathematics and Advanced Applications. Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011 Springer.
M.V. TRETYAKOV and Z. ZHANG, 2013. A fundamental mean-square convergence theorem for SDEs with locally Lipschitz coefficients and its applications SIAM J. Numer. Anal.. 51(6), 3135-3162
M.V. TRETYAKOV, 2013. Introductory Course on Financial Mathematics Imperial College Press.
BAYLISS, C.D., BIDMOS, F.A., ANJUM, A., MANCHEV, V.T., RICHARDS, R.L., GROSSIER, J., WOOLDRIDGE, K.G., KETLEY, J.M., BARROW, P.A., JONES, M.A. and TRETYAKOV, M.V., 2012. Phase Variable Genes Of Campylobacter Jejuni Exhibit High Mutation Rates And Specific Mutational Patterns But Mutability Is Not The Major Determinant Of Population Structure During Host Colonization. Nucleic Acids Research. 40(13), 82152
MILSTEIN, GN and TRETYAKOV, MV, 2012. Solving The Dirichlet Problem For Navier-Stokes Equations By Probabilistic Approach Bit Numerical Mathematics. 52(1), 141-153
Z. ZHANG, B. ROZOVSKII, M.V. TRETYAKOV and G. KARNIADAKIS, 2012. A multi-stage Wiener chaos expansion method for stochastic advection-diffusion-reaction equations Siam Journal On Scientific Computing. 34(2), A914-A936
G.N. MILSTEIN and M.V. TRETYAKOV, 2011. Averaging over characteristics with innovation approach in nonlinear filtering. In: Handbook of Nonlinear Filtering (Eds. D. Crisan and B. Rozovskii) Oxford University Press. 892-919
V.N. STANCIULESCU and M.V. TRETYAKOV, 2011. Numerical solution of the Dirichlet problem for linear parabolic SPDEs based on averaging over characteristics. In: Stochastic Analysis 2010 (Ed. D. Crisan) Springer. 191-212
MATTINGLY, J.C., STUART, A.M. and TRETYAKOV, M.V., 2010. Convergence of numerical time-averaging and stationary measures via Poisson equations SIAM Journal on Numerical Analysis. 48(2), 552-577
MENTINK, J.H., TRETYAKOV, M.V., FASOLINO, A., KATSNELSON, M.I. and RASING, T., 2010. Stable and fast semi-implicit integration of the stochastic Landau–Lifshitz equation Journal of Physics: Condensed Matter. 22(17), 176001
HARDWICK, RJ, TRETYAKOV, MV and DUBROVA, YE, 2009. Age-Related Accumulation Of Mutations Supports A Replication-Dependent Mechanism Of Spontaneous Mutation At Tandem Repeat Dna Loci In Mice Molecular Biology And Evolution. 26(11), 2647-2654
MILSTEIN, G.N. and TRETYAKOV, M.V., 2009. Solving parabolic stochastic partial differential equations via averaging over characteristics Mathematics of Computation. 78(268), 2075-2106
DAVIDCHACK, RL, HANDEL, R and TRETYAKOV, MV, 2009. Langevin Thermostat For Rigid Body Dynamics Journal Of Chemical Physics. 130(23), -
MILSTEIN, G.N. and TRETYAKOV, M.V., 2009. Practical variance reduction via regression for simulating diffusions SIAM Journal on Numerical Analysis. 47(2), 887-910
MILSTEIN, GN and TRETYAKOV, MV, 2009. Monte Carlo Methods For Backward Equations In Nonlinear Filtering Advances In Applied Probability. 41(1), 63-100
MILSTEIN, GN and TRETYAKOV, MV, 2007. Computing Ergodic Limits For Langevin Equations Physica D-Nonlinear Phenomena. 229(1), 81-95
FEDOTOV, S, MILSTEIN, GN and TRETYAKOV, MV, 2007. Superdiffusion Of A Random Walk Driven By An Ergodic Markov Process With Switching Journal Of Physics A-Mathematical And Theoretical. 40(22), 5769-5782
MILSTEIN, GN and TRETYAKOV, MV, 2007. Discretization Of Forward-Backward Stochastic Differential Equations And Related Quasi-Linear Parabolic Equations Ima Journal Of Numerical Analysis. 27(1), 24-44
MILSTEIN, GN and TRETYAKOV, MV, 2006. Numerical Algorithms For Forward-Backward Stochastic Differential Equations Siam Journal On Scientific Computing. 28(2), 561-582
MILSTEIN, GN and TRETYAKOV, MV, 2005. Numerical Integration Of Stochastic Differential Equations With Nonglobally Lipschitz Coefficients Siam Journal On Numerical Analysis. 43(3), 1139-1154
G.N. MILSTEIN and M.V. TRETYAKOV, 2005. Numerical analysis of Monte Carlo evaluation of Greeks by finite differences. Journal of Computational Finance. 8(3), 1-33
MILSTEIN, GN and TRETYAKOV, MV, 2004. Evaluation Of Conditional Wiener Integrals By Numerical Integration Of Stochastic Differential Equations Journal Of Computational Physics. 197(1), 275-298
G.N. MILSTEIN and M.V. TRETYAKOV, 2004. Stochastic Numerics for Mathematical Physics. Springer.
MILSTEIN, GN and TRETYAKOV, MV, 2003. Quasi-Symplectic Methods For Langevin-Type Equations Ima Journal Of Numerical Analysis. 23(4), 593-626
MILSTEIN, GN and TRETYAKOV, MV, 2002. The Simplest Random Walks For The Dirichlet Problem Theory Of Probability And Its Applications. 47(1), 53-68
MILSTEIN, GN, REPIN, YM and TRETYAKOV, MV, 2002. Numerical Methods For Stochastic Systems Preserving Symplectic Structure Siam Journal On Numerical Analysis. 40(4), 1583-1604
MILSTEIN, GN and TRETYAKOV, MV, 2002. A Probabilistic Approach To The Solution Of The Neumann Problem For Nonlinear Parabolic Equations Ima Journal Of Numerical Analysis. 22(4), 599-622
MILSTEIN, GN, REPIN, YM and TRETYAKOV, MV, 2002. Symplectic Integration Of Hamiltonian Systems With Additive Noise Siam Journal On Numerical Analysis. 39(6), 2066-2088
TRETYAKOV, MV and FEDOTOV, S, 2001. On The Fkpp Equation With Gaussian Shear Advection Physica D. 159(3-4), 190-201
MILSTEIN, GN and TRETYAKOV, MV, 2001. Numerical Solution Of The Dirichlet Problem For Nonlinear Parabolic Equations By A Probabilistic Approach Ima Journal Of Numerical Analysis. 21(4), 887-917
MILSTEIN, GN and TRETYAKOV, MV, 2000. Numerical Analysis Of Noise-Induced Regular Oscillations Physica D. 140(3-4), 244-256
MILSTEIN, GN and TRETYAKOV, MV, 2000. Numerical Algorithms For Semilinear Parabolic Equations With Small Parameter Based On Approximation Of Stochastic Equations Mathematics Of Computation. 69(229), 237-267
MILSTEIN, GN and TRETYAKOV, MV, 1999. Simulation Of A Space-Time Bounded Diffusion Annals Of Applied Probability. 9(3), 732-779
MILSTEIN, GN and TRETYAKOV, MV, 1999. Mean Velocity Of Noise-Induced Transport In The Limit Of Weak Periodic Forcing Journal Of Physics A-Mathematical And General. 32(31), 5795-5805
TRETYAKOV, MV, 1998. Numerical Technique For Studying Stochastic Resonance Physical Review E. 57(4), 4789-4794
MILSTEIN, GN and TRETYAKOV, MV, 1997. Numerical Methods In The Weak Sense For Stochastic Differential Equations With Small Noise Siam Journal On Numerical Analysis. 34(6), 2142-2167
MILSTEIN, GN and TRETYAKOV, MV, 1997. Mean-Square Numerical Methods For Stochastic Differential Equations With Small Noises Siam Journal On Scientific Computing. 18(4), 1067-1087
MILSHTEIN, GN and TRETYAKOV, MV, 1994. Numerical-Solution Of Differential-Equations With Colored Noise Journal Of Statistical Physics. 77(3-4), 691-715
TRETYAKOV, MV and TRETJAKOV, SV, 1994. Numerical-Integration Of Hamiltonian-Systems With External Noise Physics Letters A. 194(5-6), 371-374
BUYEVICH, YA and TRETYAKOV, MV, 1994. The Initiating Rate Of A Heterogeneous Reaction Journal De Physique Ii. 4(9), 1605-1616
BUYEVICH, YA, FEDOTOV, SP and TRETYAKOV, MV, 1993. Heterogeneous Reaction Affected By External Noise Physica A. 198(3-4), 354-367
BUYEVICH, YA and TRETYAKOV, MV, 1992. Covering Of Solid-Surface By A New Phase Under Conditions Of Metastability Reduction By Growing Nuclei Doklady Akademii Nauk. 323(2), 306-310
BUYEVICH, YA, TRETYAKOV, MV and FEDOTOV, SP, 1991. A Model Of The Stochastic Growth Of New Phase Islands On Solid-Surface Doklady Akademii Nauk Sssr. 321(5), 1005-1008
FEDOTOV, SP and TRETYAKOV, MV, 1991. Stochastic Criteria For Ignition Of Single Particles Combustion Science And Technology. 78(1-3), 1-6
FEDOTOV, SP and TRETYAKOV, MV, 1991. Stochastic Particle Combustion Khimicheskaya Fizika. 10(2), 238-241
TRETYAKOV, MV and FEDOTOV, SP, 1990. Stationary Regimes Of Heterogeneous Reaction In The Presence Of White Poisson Noise Khimicheskaya Fizika. 9(2), 252-257