Journal Articles - published
1. Fedotov, S.P. and Tret'yakov, M.V. (1988): Stationary regimes of heterogeneous chemical reaction at existence of external noises. Khimicheskay Fizika, V. 7, No. 11, pp. 1533-1537 (in Russian).
2. Tret'yakov, M.V. and Fedotov, S.P. (1990): Stationary regimes of heterogeneous chemical reaction at existence of white Poissonian noise. Khimicheskay Fizika, V. 9, No. 2, pp. 252-257 (in Russian).
3. Fedotov, S.P. and Tret'yakov, M.V. (1991): About stochastic ignition of a particle. Khimicheskay Fizika, V. 10, No. 2, pp. 238-241 (in Russian).
5. Buyevich, Yu.A., Tret'yakov, M.V., and Fedotov, S.P. (1991): Model of stochastic growth of new phase islands on solid surface. Dokl. Akad. Nauk SSSR, V. 321, No. 5, pp. 1005-1009 (in Russian); translation in Dokl. Phys. Chem., V. 6, pp. 852-854 (1991).
6. Buyevich, Yu.A. and Tret'yakov, M.V. (1992): Covering of solid surface by a new phase under conditions of metastability reduction by growing nuclei. Dokl. Akad. Nauk, V. 323, No. 2, pp. 306-310 (in Russian).
7. Tret'yakov, M.V. (1992): Influence of colored noise on combustion of a particle. Ingenerno-Fizicheskii Journal, V. 63, No. 2, pp. 156-160 (in Russian). Translated in English: Journal of Engineering Physics and Thermophysics, pp 771-774.
16. Milstein, G.N. and Tretyakov, M.V. (1999): Mean velocity of noise-induced transport in the limit of weak periodic forcing. Journal of Physics A: Mathematical and General, V. 32, No. 31, pp. 5795-5805.
17. Milstein, G.N. and Tretyakov, M.V. (2000): Numerical algorithms for semilinear parabolic equations with small parameter based on approximation of stochastic equations. Mathematics of Computation, V. 69, No. 229, pp. 237-267.
27. Milstein, G.N. and Tretyakov, M.V. (2004): Evaluation of conditional Wiener integrals by numerical integration of stochastic differential equations. Journal of Computational Physics, V. 197, No 1, pp. 275-298.
31. Milstein, G.N. and Tretyakov, M.V. (2007): Discretization of forward-backward stochastic differential equations and related quasilinear parabolic equations. IMA J Numer. Anal. V. 27, No 1, pp. 24-44.
33. Fedotov S., Milstein, G.N. and Tretyakov, M.V. (2007): Superdiffusion of a random walk driven by ergodic Markov process with switching. Journal of Physics A: Mathematical and Theoretical, V. 40, pp. 5769-5782.
38. Robert J. Hardwick, Michael V. Tretyakov, and Yuri E. Dubrova (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. V. 26, No 11, pp. 2647-2654.
39. Jonathan C. Mattingly, Andrew M. Stuart, and M.V. Tretyakov (2010): Convergence of numerical time-averaging and stationary measures via Poisson equations. SIAM J. Numer. Anal. V. 48, No 2, pp. 552-577.
40. J.H. Mentink, M.V. Tretyakov, A. Fasolino, M.I. Katsnelson, Th. Rasing (2010): Stable and fast semi-implicit integration of the stochastic Landau-Lifshitz equation. J. Phys.: Condens. Matter V. 22, Number 17, 176001 (12pp). [included in Highlights of 2010 of the journal] [SIA and SIB integrators are included in UppASD library]
43. 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 J. Sci. Comp. V. 34, No 2, pp. A914-A936.
44. Bayliss C., Bidmos F., Anjum A., Manchev V., Richards R., Grossier J-P.; Wooldridge K., Ketley J., Barrow P., Jones M., 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 colonisation. Nucleic Acids Research V 40, No. 13, pp. 5876-5889.
45. Milstein G.N. and Tretyakov M.V. (2013): Probabilistic methods for the incompressible Navier‒Stokes equations with space periodic conditions. Advances in Applied Probability, V. 45, No. 3, pp. 742-772.
46. Tretyakov M.V. and Zhang Z. (2013): A fundamental mean-square convergence theorem for SDEs with locally Lipschitz coefficients and its applications. SIAM J. Numer. Anal. V. 51, No 6, pp. 3135-3162.
48. Zhang Z., Tretyakov M.V., Rozovskii B.L. and Karniadakis G. (2014): A recursive sparse grid collocation method for differential equations with white noise. SIAM J. Sci. Comp. V. 36, No 4, pp. A1652-A1677.
50. Zhang Z., Tretyakov M.V., Rozovskii B.L. and Karniadakis G. (2015): Wiener chaos vs stochastic collocation methods for linear advection-diffusion-reaction equations with multiplicative white noise. SIAM J. Numer. Anal. V. 53, No 1, pp. 153-183.
[Langevin C integrator is implemented in LAMMPS]
52. Park M. and Tretyakov M.V. (2015): A block circulant embedding method for simulation of stationary Gaussian random fields on block-regular grids. Int. J. Uncertainty Quantification, V. 5, No. 6, pp. 527-544.
55. Davidchack R.L., Ouldridge T.E., and Tretyakov M.V. (2017): Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions. J. Chem. Phys. Vol.147, Issue 22, 224103, 12pp+5pp of Suppl Mat. +videos [also downloadable from arxiv]
56. Matveev M.Y., Ball F., Jones I.A., Long A.C., Schubel P.J., Tretyakov M.V. (2018): Uncertainty in geometry of fibre preforms manufactured with Automated Dry Fibre Placement (ADFP) and its effects on permeability. Journal of Composite Materials V.52, Issue 16, pp. 2255-2269.
57. Bailey N.Y, Hibberd S., Power H., 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 Vol. 112, Issue 1, pp. 17-35.
61. Milstein G.N. and Tretyakov M.V. (2020): Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation. Numerical Mathematics: Theory, Methods and Applications V. 14, Issue 1, pp. 1-30
62. Matveev, M.Y., Endruweit, A., Long, A.C., Iglesias, M.A, Tretyakov, M.V. (2021): Bayesian inversion algorithm for estimating local variations in permeability and porosity of reinforcements using experimental data. Composites Part A V. 143, 106323.
64. Endruweit, A., Matveev, M.Y., Tretyakov, M.V. (2022): Controlling resin flow in liquid composite moulding processes through localised irradiation with ultraviolet light. Polymer Composites V. 43, Issue 11, pp. 8308-8321.
66. Kalise, D., Sharma, A., Tretyakov, M.V. (2023): Consensus based optimization via jump-diffusion stochastic differential equations. Mathematical Models and Methods in Applied Sciences (M3AS) V. 33, No. 2, pp. 289-339 [earlier version downloadable from arxiv]
[a version is downloadable from arxiv]
69. Su, H., Tretyakov, M.V., Newton, D.P. (2024): Deep learning of transition probability densities for stochastic asset models with applications in option pricing. Management Science (accepted) (an earlier version is available at [downloadable from arxiv])
Refereed contributions to books
70. Milstein, G.N. and Tretyakov, M.V. (2011): Averaging over characteristics with innovation approach in nonlinear filtering. In Handbook of Nonlinear Filtering (Eds. D. Crisan and B. Rozovskii) Oxford University Press, ISBN 978-0-19-953290-2, pp. 892-919.
71. Stanciulescu, V.N. and Tretyakov, M.V. (2011): Numerical solution of the Dirichlet problem for linear parabolic SPDEs based on averaging over characteristics. In Stochastic Analysis 2010 (Ed. D. Crisan), Springer, ISBN 978-3-642-15357-0, pp. 191-212.
72. Krivko M. and Tretyakov M.V. (2013): Application of simplest random walk algorithms for pricing barrier options. In: Recent Developments in Computational Finance (Eds. T. Gerstner and P.E. Kloeden), World Scientific, ISBN 978-981-4436-42-7, pp. 407-428. [pre-publication is at arxiv]
73. Bailey N.Y, Hibberd S., Power H., Tretyakov M.V. (2019): Effect of uncertainty in external forcing on a fluid lubricated bearing. In: Cavalca K., Weber H. (eds) Proceedings of the 10th International Conference on Rotor Dynamics - IFToMM. IFToMM 2018. Mechanisms and Machine Science, vol 63. Springer.
74. Maurer, S., Sharp, T.E., and Tretyakov, M.V. (2021): Pricing FX options under intermediate currency. [downloadable from arxiv]
Numerical Mathematics and Advanced Applications. Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011. Cangiani, A.; Davidchack, R.L.; Georgoulis, E.; Gorban, A.N.; Levesley, J.; Tretyakov, M.V. (Eds.), Springer 2013; VIII, 854 pp. ISBN 978-3-642-33133-6.
Milstein G.N. and Tretyakov M.V. (2012): Layer methods for Navier-Stokes equations with additive noise. Research Report No. MA-12-001, Department of Mathematics, University of Leicester, Leicester (UK), 2012, 35pp. [downloadable from arxiv]