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Stochastic Evolution Systems
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Stochastic Navier-Stokes Equations for Turbulent Flows
This paper concerns the fluid dynamics modelled by the stochastic flow \left\{ \begin{array}{l} \boldsymbol{\dot{\eta}}\left( t,x\right) =\boldsymbol{u}\left( t,\boldsymbol{\eta} \left( t,x\right)Expand
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  • Open Access
On asymptotic properties of maximum likelihood estimators for parabolic stochastic PDE's
SummaryWe investigate asymptotic properties of the maximum likelihood estimators for parameters occurring in parabolic SPDEs of the form $$du(t,x) = (A_0 + \theta A_1 )u(t,x)dt + dW(t,x),$$ whereA0Expand
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Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
In this paper, we propose a numerical method based on Wiener Chaos expansion and apply it to solve the stochastic Burgers and Navier-Stokes equations driven by Brownian motion. The main advantage ofExpand
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  • Open Access
Nonlinear Filtering Revisited: A Spectral Approach
The objective of this paper is to develop an approach to nonlinear filtering based on the Cameron--Martin version of Wiener chaos expansion. This approach gives rise to a new numerical scheme forExpand
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  • Open Access
A novel approach to detection of intrusions in computer networks via adaptive sequential and batch-sequential change-point detection methods
Large-scale computer network attacks in their final stages can readily be identified by observing very abrupt changes in the network traffic. In the early stage of an attack, however, these changesExpand
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  • Open Access
The Oxford Handbook of Nonlinear Filtering
In many areas of human endeavour, the systems involved are not available for direct measurement. Instead, by combining mathematical models for a system's evolution with partial observations of itsExpand
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A Simple Proof of Uniqueness for Kushner and Zakai Equations
Publisher Summary This chapter presents a simple proof of uniqueness for a generalized solution to the Kushner and Zakai equations for diffusion processes. These solutions are considered in the spaceExpand
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A filtering approach to tracking volatility from prices observed at random times
This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $ S=(S_{t})_{t\geq0} $Expand
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  • Open Access
Weighted Stochastic Sobolev Spaces and Bilinear SPDEs Driven by Space–Time White Noise
In this paper we develop basic elements of Malliavin calculus on a weightedL2(Ω). This class of generalized Wiener functionals is a Hilbert space. It turns out to be substantially smaller than theExpand
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