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Uniqueness Of The Solution For Zakai ‘S Equation
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Abstract
In this chapter, we prove the uniqueness of the solution to Zakai ‘s equation by transforming it to an SDE in a Hilbert space and by making use of estimates based on Hilbert-space techniques. Most of the material in Sections 6.2–6.4 is taken from Kurtz and Xiong [97] where a large class of linear stochastic partial differential equations are studied. Although the techniques we introduce here are for Zakai ‘s equation, they can be applied to other classes of linear SPDEs that includes Zakai ‘s equation as a special example.
Title: Uniqueness Of The Solution For Zakai ‘S Equation
Description:
Abstract
In this chapter, we prove the uniqueness of the solution to Zakai ‘s equation by transforming it to an SDE in a Hilbert space and by making use of estimates based on Hilbert-space techniques.
Most of the material in Sections 6.
2–6.
4 is taken from Kurtz and Xiong [97] where a large class of linear stochastic partial differential equations are studied.
Although the techniques we introduce here are for Zakai ‘s equation, they can be applied to other classes of linear SPDEs that includes Zakai ‘s equation as a special example.
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