| Abstract: |
| The objective in stochastic filtering is to reconstruct
the information about an unobserved (random) process, called the
signal process, given the current available observations of a
certain noisy transformation of that process, called observation process.
Usually $X$ and $Y$ are modeled by stochastic differential equations driven by
a Brownian motion or a jump (or L\`evy) process.
We are interested in the situation where both
the state process $X$ and the observation process $Y$ are
perturbed by coupled Levy processes.
In the talk we first present some theoretical results. More precisely,
we consider the situation where $L=(L_1,L_2)$ is a $2$--dimensional Levy process in which the
structure of dependence is described by a Levy copula. $L_1$ appears in the signal process, $L_2$ appears in the observation process.
Secondly, we introduce the approximation of the density by a particle system. |
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