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Professor MIKHAIL TRETYAKOV's Outputs (20)

Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications (2025)
Journal Article
Hinds, P. D., Sharma, A., & Tretyakov, M. V. (in press). Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications. Mathematical Models and Methods in Applied Sciences,

In this paper, we establish well-posedness of reflected McKean-Vlasov SDEs and their particle approximations in smooth non-convex domains. We prove convergence of the interacting particle system to the corresponding mean-field limit with the optimal... Read More about Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications.

Sampling from mixture distributions based on regime-switching diffusions (2025)
Journal Article
Tretyakov, M. V. (in press). Sampling from mixture distributions based on regime-switching diffusions. SIAM Journal on Scientific Computing,

It is proposed to use stochastic differential equations with state-dependent switching 4 rates (SDEwS) for sampling from finite mixture distributions. An Euler scheme with constant time 5 step for SDEwS is considered. It is shown that the scheme conv... Read More about Sampling from mixture distributions based on regime-switching diffusions.

Deep Learning of Transition Probability Densities for Stochastic Asset Models with Applications in Option Pricing (2024)
Journal Article
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, https://doi.org/10.1287/mnsc.2022.01448

Transition probability density functions (TPDFs) are fundamental to computational finance, including option pricing and hedging. Advancing recent work in deep learning, we develop novel neural TPDF generators through solving backward Kolmogorov equat... Read More about Deep Learning of Transition Probability Densities for Stochastic Asset Models with Applications in Option Pricing.

Neural variance reduction for stochastic differential equations (2023)
Journal Article
Hinds, P., & Tretyakov, M. (2023). Neural variance reduction for stochastic differential equations. Journal of Computational Finance, 27(3), 1-41. https://doi.org/10.21314/JCF.2023.010

Variance reduction techniques are of crucial importance for the efficiency of Monte Carlo simulations in finance applications. We propose the use of neural SDEs, with control variates parameterized by neural networks, in order to learn approximately... Read More about Neural variance reduction for stochastic differential equations.

Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions (2023)
Journal Article
Leimkuhler, B., Sharma, A., & Tretyakov, M. V. (2023). Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions. Annals of Applied Probability, 33(3), 1904-1960. https://doi.org/10.1214/22-AAP1856

A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed. It is proved that the method has the first order of weak convergence. Together with the Monte Carlo techniq... Read More about Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions.

Consensus-based optimization via jump-diffusion stochastic differential equations (2023)
Journal Article
Kalise, D., Sharma, A., & Tretyakov, M. V. (2023). Consensus-based optimization via jump-diffusion stochastic differential equations. Mathematical Models and Methods in Applied Sciences, 33(02), 289-339. https://doi.org/10.1142/S0218202523500082

We introduce a new consensus-based optimization (CBO) method where an interacting particle system is driven by jump-diffusion stochastic differential equations (SDEs). We study well-posedness of the particle system as well as of its mean-field limit.... Read More about Consensus-based optimization via jump-diffusion stochastic differential equations.

Ensemble Kalman inversion for magnetic resonance elastography. (2022)
Journal Article
Iglesias, M., McGrath, D. M., Tretyakov, M. V., & Francis, S. T. (2022). Ensemble Kalman inversion for magnetic resonance elastography. Physics in Medicine and Biology, 67(23), Article 235003. https://doi.org/10.1088/1361-6560/ac9fa1

Magnetic Resonance Elastography (MRE) is an MRI-based diagnostic method for measuring mechanical properties of biological tissues. MRE measurements are processed by an inversion algorithm to produce a map of the biomechanical properties. In this pape... Read More about Ensemble Kalman inversion for magnetic resonance elastography..

Controlling resin flow in Liquid Composite Moulding processes through localized irradiation with ultraviolet light (2022)
Journal Article
Endruweit, A., Matveev, M., & Tretyakov, M. V. (2022). Controlling resin flow in Liquid Composite Moulding processes through localized irradiation with ultraviolet light. Polymer Composites, 43(11), 8308-8321. https://doi.org/10.1002/pc.27001

A vacuum infusion process was implemented to produce composite specimens from a random glass filament mat and an acrylic modified polyester resin curable upon irradiation with ultraviolet (UV) light. Through localized irradiation with UV light during... Read More about Controlling resin flow in Liquid Composite Moulding processes through localized irradiation with ultraviolet light.

Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation (2020)
Journal Article
Milstein, G. N., & Tretyakov, M. V. (2021). Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation. Numerical Mathematics, 14(1), 1-30. https://doi.org/10.4208/nmtma.OA-2020-0034

We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals r... Read More about Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation.

Effect of random forcing on fluid lubricated bearing (2019)
Journal Article
Bailey, N., Hibberd, S., Tretyakov, M., & Power, H. (2019). Effect of random forcing on fluid lubricated bearing. IMA Journal of Applied Mathematics, 84(3), 632–649. https://doi.org/10.1093/imamat/hxz007

A model for a fluid lubricated bearing is derived for operation under conditions where external forces are subject to random fluctuations that may act to destabilise the bearing. The fluid flow through the bearing is described by a Reynolds equation... Read More about Effect of random forcing on fluid lubricated bearing.

Bayesian inversion in resin transfer molding (2018)
Journal Article
Iglesias, M., Park, M., & Tretyakov, M. (2018). Bayesian inversion in resin transfer molding. Inverse Problems, 34(10), Article 105002. https://doi.org/10.1088/1361-6420/aad1cc

We study a Bayesian inverse problem arising in the context of Resin Transfer Molding (RTM), which is a process commonly used for the manufacturing of fiber- reinforced composite materials. The forward model is described by a moving boundary problem i... Read More about Bayesian inversion in resin transfer molding.

Evaluation of the minimum face clearance of a high speed gas lubricated bearing with Navier slip boundary conditions under random excitations (2018)
Journal Article
Bailey, N., Hibberd, S., Power, H., & Tretyakov, M. (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, 112(1), 17–35. https://doi.org/10.1007/s10665-018-9963-9

Motivated by ongoing developments in aero-engine technology, a model for a coupled gas lubricated bearing is developed in terms of an extended dynamical system. A slip boundary condition, characterised by a slip length, is incorporated on the bearing... Read More about Evaluation of the minimum face clearance of a high speed gas lubricated bearing with Navier slip boundary conditions under random excitations.

Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions (2017)
Journal Article
Davidchack, R., Ouldridge, T., & Tretyakov, M. (in press). Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions. Journal of Chemical Physics, 147(22), Article 224103. https://doi.org/10.1063/1.4999771

We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces, and hydrodynamic coupling. In the absence of non-conservative forces the Langevi... Read More about Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions.

Uncertainty in geometry of fibre preforms manufactured with Automated Dry Fibre Placement and its effects on permeability (2017)
Journal Article
Matveev, M. Y., Ball, F. G., 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 and its effects on permeability. Journal of Composite Materials, 52(16), 2255-2269. https://doi.org/10.1177/0021998317741951

© 2017, The Author(s) 2017. Resin transfer moulding is one of several processes available for manufacturing fibre-reinforced composites from dry fibre reinforcement. Recently, dry reinforcements made with Automated Dry Fibre Placement have been intro... Read More about Uncertainty in geometry of fibre preforms manufactured with Automated Dry Fibre Placement and its effects on permeability.

Stochastic resin transfer molding process (2017)
Journal Article
Park, M., & Tretyakov, M. (in press). Stochastic resin transfer molding process. SIAM/ASA Journal on Uncertainty Quantification, 5(1), https://doi.org/10.1137/16M1096578

We consider one-dimensional and two-dimensional models of the stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and numerically in t... Read More about Stochastic resin transfer molding process.

Layer methods for stochastic Navier–Stokes equations using simplest characteristics (2016)
Journal Article
Milstein, G., & Tretyakov, M. (2016). Layer methods for stochastic Navier–Stokes equations using simplest characteristics. Journal of Computational and Applied Mathematics, 302, https://doi.org/10.1016/j.cam.2016.01.051

We propose and study a layer method for stochastic Navier-Stokes equations (SNSE) with spatial periodic boundary conditions and additive noise. The method is constructed using conditional probabilistic representations of solutions to SNSE and exploit... Read More about Layer methods for stochastic Navier–Stokes equations using simplest characteristics.

A recursive sparse grid collocation method for differential equations with white noise (2014)
Journal Article
Zhang, Z., Tretyakov, M., Rozovskii, B., & Karniadakis, G. E. (2014). A recursive sparse grid collocation method for differential equations with white noise. SIAM Journal on Scientific Computing, 36(4), A1652–A1677. https://doi.org/10.1137/130938906

We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise. We first an... Read More about A recursive sparse grid collocation method for differential equations with white noise.

On the long-time integration of stochastic gradient systems (2014)
Journal Article
Leimkuhler, B., Matthews, C., & Tretyakov, M. (2014). On the long-time integration of stochastic gradient systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470(2170), Article 20140120. https://doi.org/10.1098/rspa.2014.0120

This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic (stepsize... Read More about On the long-time integration of stochastic gradient systems.