# Questions tagged [stochastic-filtering]

Stochastic filtering deals with the problem of finding the best estimate for a signal, given a noisy or incomplete observation.

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### Reference: Stochastic Filtering Infinite Dimensions

I've come across these Hilbert Space Signal Finite Dimensional Measurements and Linear Gaussian Hilbert space signal and measurements.
Is there any literature solving the Zakai equation when both ...

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### Ergodicity of differentiated processes

Let $S$ be a vector space, and $X$ a jointly-measurable random process/field with two parameters:
$$ X: [0,\infty)\times\mathbb{R}\times\Omega\to S,$$
i.e. $X_{t,\theta}:\Omega\to S$ are random ...

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### A conjecture in rate distortion theory and stochastic filtering

Let $(X_t)_{t\in T}$ be a stationary random process with known and fixed law $P_X$ describing a dynamic source.
This source is to be encoded real-time by an encoder $e$ into an encoded message $E_t$ ...

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### 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(d stochastic process). You can consider the unnormalized version $V_t$.
The ...

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### Filtering Mixed Discrete and Continous

Suppose I have signal process $\lambda_t$ following the dynamics
\begin{equation}
\begin{aligned}
\zeta_t&=\mu^{\zeta}(t,{\zeta}_t)dt+\sigma^{\zeta}(t,{\zeta}_t)dW^{\zeta}_t\\
\xi_t&=\mu^{\xi}(...