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.
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 [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. Vol. 52
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.
Refereed contributions to books
59. 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.
60. 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.
61. 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]
62. Bailey N.Y, Hibberd S., Power H., Tretyakov M.V. (2018): Effect of random forcing on fluid lubricated bearing.
63. Bayliss C.D., Fallaize C., Howitt R., Tretyakov M.V. (2018): Mutation and selection in bacteria: modelling and calibration. [downloadable from arxiv]
64. Milstein G.N. and Tretyakov M.V. (2018): Approximation of deterministic and stochastic Navier-Stokes equations in vorticity-velocity formulation. [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]