215 citations · 350 across the 14 of their papers we have counts for
14 papers
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 distribution free Skorokhod-Malliavin calculus
R. Mikulevicius, B. L. Rozovskii
The starting point of the current paper is a sequence of uncorrelated random variables. The distribution functions of these variables are assumed to be given but no assumptions on…
On unbiased stochastic Navier-Stokes equation
R. Mikulevicius, B. L. Rozovskii
A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an SPDE with Wick type nonlinearity. The nonlinear term of the perturbation can be char…
A Note on Generalized Malliavin Calculus
S. V. Lototsky, B. L. Rozovskii, D. Seleši
The Malliavin derivative, divergence operator, and the Ornstein-Uhlenbeck operator are extended from the traditional Gaussian setting to generalized processes from the higher-order…
A Unified Approach to Stochastic Evolution Equations Using the Skorokhod Integral
S. V. Lototsky, B. L. Rozovskii
We study stochastic evolution equations driven by Gaussian noise. The key features of the model are that the operators in the deterministic and stochastic parts can have the same o…
Stochastic Parabolic Equations of Full Second Order
S. V. Lototsky, B. L. Rozovskii
A procedure is described for defining a generalized solution for stochastic differential equations using the Cameron-Martin version of the Wiener Chaos expansion. Existence and uni…