440 citations · 905 across the 22 of their papers we have counts for
9 papers · 1 filter
Sampling from mixture distributions based on regime-switching diffusions
M. V. Tretyakov
It is proposed to use stochastic differential equations with state-dependent switching rates (SDEwS) for sampling from finite mixture distributions. An Euler scheme with constant t…
Neural variance reduction for stochastic differential equations
P. D. Hinds, M. V. Tretyakov
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 varia…
Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions
B. Leimkuhler, A. Sharma, M. V. Tretyakov
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…
Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation
G. Deligiannidis, S. Maurer, M. V. Tretyakov
We consider stochastic differential equations driven by a general Lévy processes (SDEs) with infinite activity and the related, via the Feynman-Kac formula, Dirichlet problem for p…
Approximation of deterministic and stochastic Navier-Stokes equations in vorticity-velocity formulation
G. N. Milstein, M. V. Tretyakov
We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions in the vorticity-velocity formulation. The approximation is ba…
Wiener chaos vs stochastic collocation methods for linear advection-diffusion equations with multiplicative white noise
Zhongqiang Zhang, Michael V. Tretyakov, Boris Rozovskii +1
We compare Wiener chaos and stochastic collocation methods for linear advection-reaction-diffusion equations with multiplicative white noise. Both methods are constructed based on…
On the long-time integration of stochastic gradient systems
B. Leimkuhler, C. Matthews, M. V. Tretyakov
This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on propert…
Layer methods for Navier-Stokes equations with additive noise
G. N. Milstein, M. V. Tretyakov
We propose and study a number of layer methods for stochastic Navier-Stokes equations (SNSE) with spatial periodic boundary conditions and additive noise. The methods are construct…
A fundamental mean-square convergence theorem for SDEs with locally Lipschitz coefficients and its applications
M. V. Tretyakov, Z. Zhang
A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDE) which coefficients are allowed to grow polynomially at infinity a…