Branching and interacting particle systems approximations of feynman-kac formulae with applications to non-linear filtering

Abstract

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A Survey of Sequential Monte Carlo Methods for Economics and Finance

“…The first consistency proof of the bootstrap filter was given by Del Moral (1996) with asymptotic normality established in Del Guionnet (1999) andMiclo (2000). The CLT was later extended to include more advanced algorithms in Chopin (2004) andKünsch (2005).…”

An approximate McKean-Vlasov model for the stochastic filtering problem

“…where X i,δn , i ≥ 0 are independent realizations of the non-linear diffusion X δ as defined by (10). Henceθ t has an asymptotic representation involving particles with equal weights.…”

“…For this, one would have to obtain numerical approximation for the non-linear diffusions X i,δ n i=1 . In other words, we need to solve numerically the McKean-Vlasov equation (10). An additional approximating procedure is needed for this.…”

“…In order to offset this outcome, a wealth of methods have been proposed. In filtering theory, the generic name for such a method is that of a particle filter ([4], [5], [10], etc.). The standard remedy is to introduce an additional procedure that removes particles with small weights and adds additional particles in places where the existing one have large weights.…”

SVM-Enhanced Filtering Model for Limit Order Book Dynamics

“…In practice, we take f as an identity map and employ branching particle filter to approximate the conditional distribution P(X t ∈ •|G t ) as in Del Moral and Miclo [4]. Particle filter is a method to approximate the conditional distribution P(X t ∈ •|G t ) with some suitable discrete random measures of the form P( …”