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user69208

In stochastic filtering you are interested in a process called the optimal filter $\pi_t$ which is a probability measure(d stochastic process). You can consider the unnormalized version $V_t$.

The unnormalized measure satisfies the Zakai equation, a linear stochastic PDE. The normalized measure satisfies the Kushner-FKK equation, a nonlinear stochastic PDE.

If you solve the Zakai equation, you can simply normalize to get $\pi_t$.

Is there any reason to work with the Kushner-FKK equation directly? Perhaps some numerics?

In stochastic filtering you are interested in a process called the optimal filter $\pi_t$ which is a probability measure. You can consider the unnormalized version $V_t$.

The unnormalized measure satisfies the Zakai equation, a linear stochastic PDE. The normalized measure satisfies the Kushner-FKK equation, a nonlinear stochastic PDE.

If you solve the Zakai equation, you can simply normalize to get $\pi_t$.

Is there any reason to work with the Kushner-FKK equation directly? Perhaps some numerics?

In stochastic filtering you are interested in a process called the optimal filter $\pi_t$ which is a probability measure(d stochastic process). You can consider the unnormalized version $V_t$.

The unnormalized measure satisfies the Zakai equation, a linear stochastic PDE. The normalized measure satisfies the Kushner-FKK equation, a nonlinear stochastic PDE.

If you solve the Zakai equation, you can simply normalize to get $\pi_t$.

Is there any reason to work with the Kushner-FKK equation directly? Perhaps some numerics?

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user69208
user69208

In stochastic filtering you are interested in a process called the optimal filter $\pi_t$ which is a probability measure. You can consider the unnormalized version $V_t$.

The unnormalized measure satisfies the Zakai equation, a linear stochastic PDE. The normalized measure satisfies the Kushner-FKK equation, ana nonlinear stochastic PDE.

If you solve the Zakai equation, you can simply normalize to get $\pi_t$.

Is there any reason to work with the Kushner-FKK equation directly? Perhaps some numerics?

In stochastic filtering you are interested in a process called the optimal filter $\pi_t$ which is a probability measure. You can consider the unnormalized version $V_t$.

The unnormalized measure satisfies the Zakai equation, a linear stochastic PDE. The normalized measure satisfies the Kushner-FKK equation, an nonlinear stochastic PDE.

If you solve the Zakai equation, you can simply normalize to get $\pi_t$.

Is there any reason to work with the Kushner-FKK equation directly? Perhaps some numerics?

In stochastic filtering you are interested in a process called the optimal filter $\pi_t$ which is a probability measure. You can consider the unnormalized version $V_t$.

The unnormalized measure satisfies the Zakai equation, a linear stochastic PDE. The normalized measure satisfies the Kushner-FKK equation, a nonlinear stochastic PDE.

If you solve the Zakai equation, you can simply normalize to get $\pi_t$.

Is there any reason to work with the Kushner-FKK equation directly? Perhaps some numerics?

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user69208
user69208

Why would one work with Kushner-FKK equation over Zakai equation?

In stochastic filtering you are interested in a process called the optimal filter $\pi_t$ which is a probability measure. You can consider the unnormalized version $V_t$.

The unnormalized measure satisfies the Zakai equation, a linear stochastic PDE. The normalized measure satisfies the Kushner-FKK equation, an nonlinear stochastic PDE.

If you solve the Zakai equation, you can simply normalize to get $\pi_t$.

Is there any reason to work with the Kushner-FKK equation directly? Perhaps some numerics?