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- Publications
- Influence

Stochastic Navier-Stokes Equations for Turbulent Flows

- R. Mikulevicius, B. Rozovskii
- Computer Science, Mathematics
- SIAM J. Math. Anal.
- 2004

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

On asymptotic properties of maximum likelihood estimators for parabolic stochastic PDE's

- M. Huebner, B. Rozovskii
- Mathematics
- 1 June 1995

SummaryWe investigate asymptotic properties of the maximum likelihood estimators for parameters occurring in parabolic SPDEs of the form
$$du(t,x) = (A_0 + \theta A_1 )u(t,x)dt + dW(t,x),$$
whereA0… Expand

Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics

- T. Hou, Wuan Luo, B. Rozovskii, H. Zhou
- Computer Science, Mathematics
- J. Comput. Phys.
- 10 August 2006

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 of… Expand

Nonlinear Filtering Revisited: A Spectral Approach

- S. Lototsky, R. Mikulevičius, B. Rozovskii
- Mathematics
- 1 March 1997

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 for… Expand

A novel approach to detection of intrusions in computer networks via adaptive sequential and batch-sequential change-point detection methods

- A. Tartakovsky, B. Rozovskii, Rudolf B. Blazek, H. Kim
- Mathematics, Computer Science
- IEEE Transactions on Signal Processing
- 1 September 2006

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 changes… Expand

The Oxford Handbook of Nonlinear Filtering

- D. Crisan, B. Rozovskii
- History
- 15 April 2011

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 its… Expand

- 97
- 6

A Simple Proof of Uniqueness for Kushner and Zakai Equations

- B. Rozovskii
- Mathematics
- 1991

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 space… Expand

A filtering approach to tracking volatility from prices observed at random times

- J. Cvitanic, R. Liptser, B. Rozovskii
- Mathematics, Economics
- 21 September 2005

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

Weighted Stochastic Sobolev Spaces and Bilinear SPDEs Driven by Space–Time White Noise

- D. Nualart, B. Rozovskii
- Mathematics
- 1 September 1997

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 the… Expand