Publications



Research monograph

 Milstein, G.N. and Tretyakov, M.V. (2004) Stochastic Numerics for Mathematical Physics. Series: Scientific Computation, Springer,  XX+ 596 p., 48 illus. ISBN: 3-540-21110-1.

 

Textbook

  Tretyakov, M.V. (2013) Introductory Course on Financial Mathematics, Imperial College Press,  X+ 266 p. ISBN: 978-1-908977-38-0.

 

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).

4.  Fedotov, S.P. and Tret'yakov, M.V. (1991): Stochastic criteria for ignition of single particles. Combust. Sci. and Tech., V. 78,  No. 1-3, pp. 1-6.

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.

8.  Buyevich, Yu.A., Fedotov, S.P., and Tret'yakov, M.V. (1993): Heterogeneous  reaction affected by external noise. Physica A,  V. 198, Nos. 3/4, pp. 354-367.

9.  Buyevich, Yu.A. and Tret'yakov, M.V. (1994): The initiating rate of a heterogeneous reaction. Journal de Physique II,    V. 4, pp. 1605-1616.

10. Milshtein, G.N. and  Tret'yakov, M.V. (1994): Numerical solution of differential equations with colored noise. J. Stat. Phys., V. 77, Nos. 3/4, pp. 691-715.

11. Tret'yakov, M.V. and Tret'jakov, S.V. (1994): Numerical integration of Hamiltonian systems with external noise. Phys. Lett. A, V. 194, pp. 371-374.

12. Milstein, G.N. and Tret'yakov, M.V. (1997): Mean-square numerical methods for stochastic differential equations with small noises. SIAM J. Sci. Comput., V. 18, No. 4, pp. 1067-1087.

13. Milstein, G.N. and Tret'yakov, M.V. (1997): Numerical methods in the weak sense for stochastic differential equations with small noise. SIAM J. Numer. Anal., V. 34, No. 6, pp. 2142-2167.

14. Tretyakov, M.V. (1998): Numerical technique for studying stochastic resonance. Physical Review E, V. 57, No. 4, pp. 4789-4794.

15. Milstein, G.N. and Tretyakov, M.V. (1999): Simulation of a space-time diffusion. The Annals of Applied Probability, V. 9, No. 3,   pp. 732-779.

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.

18. Milstein, G.N. and Tretyakov, M.V. (2000): Numerical analysis of noise-induced regular oscillations. Physica D: Nonlinear Phenomena, V.140, Nos. 3-4, pp. 244-256.

19. Milstein, G.N. and Tretyakov, M.V. (2001): Noise-induced unidirectional transport. Stochastics and Dynamics, V. 1, No 1, pp. 361-375.

20. Milstein, G.N. and Tretyakov, M.V. (2001): Numerical solution of Dirichlet problems for nonlinear parabolic equations by a probabilistic approach. IMA J. Num. Anal., V. 21, No 4, pp. 887-917.

21. Tretyakov, M.V. and Fedotov S. (2001): On FKPP equation with Gaussian shear advection. Physica D: Nonlinear Phenomena, V. 159, Nos. 3-4, pp. 191-202.

22. Milstein, G.N. and Tretyakov, M.V. (2002): The simplest random walks for the Dirichlet problem. Theory of Probability and its Applications  V. 47, No 1, pp. 39-58 (Russian); pp. 53-68 (English).

23. Milstein, G.N., Repin, Yu.M., and Tretyakov, M.V. (2002): Symplectic integration of Hamiltonian systems with additive noise. SIAM J. Numer. Anal. V. 39, No 6, pp. 2066-2088.

24. Milstein, G.N. and Tretyakov, M.V. (2002): A probabilistic approach to solution of the Neumann problem for nonlinear parabolic equations. IMA J. Numer. Anal., V. 22, No 4, pp. 599-622.

25. Milstein, G.N., Repin, Yu.M., and Tretyakov, M.V. (2002):  Numerical methods for stochastic systems preserving symplectic structure. SIAM J. Numer. Anal., V. 40, No 4, pp. 1583-1604.

26. Milstein, G.N. and Tretyakov, M.V. (2003): Quasi-symplectic methods for Langevin-type equations. IMA J. Numer. Anal., V. 23, No 4, pp. 593-626.

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.

28. Milstein, G.N. and Tretyakov, M.V. (2005): Numerical integration of stochastic differential equations with nonglobally Lipschitz coefficients. SIAM J. Numer. Anal., V. 43, No3, 1139-1154.

29. Milstein, G.N. and Tretyakov, M.V. (2005): Numerical analysis of Monte Carlo evaluation of Greeks by finite differences. Journal of Computational Finance, V. 8, No 3, pp. 1-33.

30. Milstein, G.N. and Tretyakov, M.V. (2006): Numerical algorithms for forward-backward stochastic differential equations. SIAM J. Sci. Comp., V. 28, No 2, pp. 561-582.

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.

32. Milstein, G.N. and Tretyakov, M.V. (2007): Computing ergodic limits for Langevin equations. Physica D: Nonlinear Phenomena, V. 129, No 1, pp. 81-95.

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.

34. Milstein, G.N. and Tretyakov, M.V. (2009): Practical variance reduction via regression for simulating diffusions. SIAM J. Numer. Anal. V. 47, No. 2, pp. 887-910.

35. Milstein, G.N. and Tretyakov, M.V. (2009): Monte Carlo algorithms for backward equations in nonlinear filtering. Advances in Applied Probability, V. 41, No. 1, pp. 63-100.

36. Milstein, G.N. and Tretyakov, M.V. (2009): Solving parabolic stochastic partial differential equations via averaging over characteristics. Math. Comp. V. 78, No 268, pp. 2075-2106.

37. Ruslan L. Davidchack, Richard Handel, and M.V. Tretyakov (2009): Langevin thermostat for rigid body dynamics. J. Chem. Phys. V. 130, Issue 23, pp. 234101-14.

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]

41. Dumas, W.M. and Tretyakov, M.V. (2011): Computing conditional Wiener integrals of functionals of a general form. IMA J. Numer. Anal. V. 31, No 3, pp. 1217-1251.

42. Milstein G.N. and Tretyakov M.V. (2012): Solving the Dirichlet problem for Navier-Stokes equations by probabilistic approach. BIT Numer. Math. V. 52 , No 1, pp. 141-153.

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): Layer 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.

47. Krivko M. and Tretyakov M.V. (2014): Numerical integration of Heath-Jarrow-Morton model of interest rates. IMA J. Numer. Anal. V. 34, pp. 147-196.

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.

49. Leimkuhler B., Matthews C., and Tretyakov M.V. (2014): On the long-time integration of stochastic gradient systems. Proc. R. Soc. A V. 470, No 2170, 20140120, 16 pp.

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.

51. Davidchack R.L., Ouldridge T.E., and Tretyakov M.V. (2015): New Langevin and gradient thermostats for rigid body dynamics. J. Chem. Phys. V. 142, No 14, 144114, 13 pp.

[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.

53. Milstein G.N. and Tretyakov M.V. (2016): Layer methods for Navier-Stokes equations with additive noise using simplest characteristics. J. Comp Appl. Maths. V. 302, pp. 1-23.

54. Park M. and Tretyakov M.V. (2017): Stochastic resin transfer molding process. SIAM/ASA Journal on Uncertainty Quantification. To appear. 27pp. [downloadable from arxiv]

 

Refereed contributions to books

55. 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.

56. 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.

57. 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]

 

Recent preprints

58. Matveev M.Y., Ball F., Jones I.A., Long A.C., Schubel P.J., Tretyakov M.V. (2017): Uncertainty in geometry of fibre preforms manufactured with Automated Dry Fibre Placement (ADFP) and its effects on permeability.

59. Bailey N.Y, Hibberd S., Power H., Tretyakov M.V. (2017): Dynamics of a high speed gas lubricated bearing with Navier slip boundary conditions under random excitations.

60. Iglesias M., Park M., Tretyakov M.V. (2017): Bayesian inversion in resin transfer molding. [downloadable from arxiv]

61. 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. [downloadable from arxiv]

Book Editor

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.

 

Other

Tretyakov M.V. (2015): Stochastic filtering. In Encyclopedia of Applied and Computational Mathematics, Editor-in-Chief Bjorn Engquist, Springer, ISBN 978-3-540-70530-7.

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]