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.
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).
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).
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. (accepted)
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 (accepted)
Refereed contributions to books
45. 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.
46.
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.
Recent preprints
47. Milstein G.N. and Tretyakov M.V. (2010): Layer methods for the
incompressible Navier-Stokes equations with space periodic conditions. Research
Report No. MA-10-012, Department of Mathematics, University of Leicester,
Leicester (UK), 2010, 27pp.
48. Krivko M. and Tretyakov M.V. (2011): Numerical integration of
Heath-Jarrow-Morton model of interest rates. Research Report No. MA-11-001,
Department of Mathematics, University of Leicester, Leicester (UK), 2011, 48pp.
[downloadable
from SSRN]
49. 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.