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. Vol. 5, No. 1, pp. 1110-1135. [also downloadable from arxiv]

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.

58. Iglesias M., Park M., Tretyakov M.V. (2018): Bayesian inversion in resin transfer molding. Inverse Problems.

 

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]

 

Recent preprints

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]

 

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]