# An Estimation Problem for Quasilinear Stochastic Partial Differential Equations

An Estimation Problem for Quasilinear Stochastic Partial Differential Equations A problem of estimating a functional parameter θ(x) and functionals Φ(θ) based on observation of a solution u ε(t, x) of the stochastic partial differential equation $$du_\varepsilon (t)= \sum\limits_{|k| \leqslant 2p} a_k D_x^k u_\varepsilon dt+ \theta (x)g(u_\varepsilon,t,x)+\varepsilon dw(t)$$ is considered. The asymptotic problem setting, as the noise intensity ε → 0, is investigated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# An Estimation Problem for Quasilinear Stochastic Partial Differential Equations

, Volume 39 (1) – Oct 4, 2004
27 pages

/lp/springer_journal/an-estimation-problem-for-quasilinear-stochastic-partial-differential-MSknIt8ugH
Publisher
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/A:1023630515274
Publisher site
See Article on Publisher Site

### Abstract

A problem of estimating a functional parameter θ(x) and functionals Φ(θ) based on observation of a solution u ε(t, x) of the stochastic partial differential equation $$du_\varepsilon (t)= \sum\limits_{|k| \leqslant 2p} a_k D_x^k u_\varepsilon dt+ \theta (x)g(u_\varepsilon,t,x)+\varepsilon dw(t)$$ is considered. The asymptotic problem setting, as the noise intensity ε → 0, is investigated.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 4, 2004

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