Professor MIKHAIL TRETYAKOV's Outputs (2)

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.