TY - CHAP

T1 - Low-Noise Analysis of Zakai’s Equation

AU - Schuss, Zeev

N1 - Publisher Copyright:
© Springer Science+Business Media, LLC 2012.

PY - 2012

Y1 - 2012

N2 - Zakai’s equation is a stochastic linear parabolic initial value problem that except for the linear case, has a closed-form solution only in exceptional and not very useful cases [165]. To understand the difficulties in applying the Zakai equation to the filtering problem, we consider again the simplified one-dimensional filtering problem (3.22), (3.23), 4.1.

AB - Zakai’s equation is a stochastic linear parabolic initial value problem that except for the linear case, has a closed-form solution only in exceptional and not very useful cases [165]. To understand the difficulties in applying the Zakai equation to the filtering problem, we consider again the simplified one-dimensional filtering problem (3.22), (3.23), 4.1.

KW - Conditional Moment

KW - Extended Kalman Filter

KW - Optimal Filter

KW - Riccati Equation

KW - Stochastic Differential Equation

UR - http://www.scopus.com/inward/record.url?scp=85068188360&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-0487-3_4

DO - 10.1007/978-1-4614-0487-3_4

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AN - SCOPUS:85068188360

T3 - Applied Mathematical Sciences (Switzerland)

SP - 107

EP - 145

BT - Applied Mathematical Sciences (Switzerland)

PB - Springer

ER -