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As the name suggests, Stochastic Partial Differential Equations is an interdisciplinary area at the crossroads of stochastic processes and partial differential equations (SPDEs). The beginnings of… (More)

- Mengdi Zheng, Boris Rozovsky, George Em Karniadakis
- SIAM J. Scientific Computing
- 2015

We propose an adaptive Wick--Malliavin (WM) expansion in terms of the Malliavin derivative of order $Q$ to simplify the propagator of general polynomial chaos (gPC) of order $P$ (a system of… (More)

Let us fix \(T_{0},T\in \mathbb {R}_{+}\) with T0 ≤ T, and \(\mathrm {d},\mathrm {d}_1\in \mathbb {N}\). We also fix the stochastic basis \(\mathbb {F}=(\varOmega , \mathscr {F}, \{\mathscr… (More)

Let U = U(t, x) be the temperature of the top layer of a body of water such as lake, sea, or ocean. Various historical data provide information about the long-time average value \(\bar{U}\) of U.

There are many standard references on SODEs and even more standard references on deterministic PDEs. Here are a few of each, listed in a non-decreasing order of difficulty:

This chapter contains somewhat abstract but necessary, material on functional analysis and stochastic calculus. To save time, one can move on to the following chapters and come back as necessary.

- Boris Rozovsky
- 2016

The first of the four sections in this chapter presents examples of linear stochastic evolution systems (LSESs) arising in various applications. The following three sections collect a number of… (More)