Dimension-free Wasserstein contraction of nonlinear filters

Research output: Contribution to journalArticle (Academic Journal)

Abstract

For a class of partially observed diffusions, conditions are given for the map from the initial condition of the signal to filtering distribution to be contractive with respect to Wasserstein distances, with rate which does not necessarily depend on the dimension of the state-space. The main assumptions are that the signal has affine drift and constant diffusion coefficient and that the likelihood functions are log-concave. Ergodic and nonergodic signals are handled in a single framework. Examples include linear-Gaussian, stochastic volatility, neural spike-train and dynamic generalized linear models. For these examples filter stability can be established without any assumptions on the observations.
Original languageEnglish
Pages (from-to)31-50
Number of pages20
JournalStochastic Processes and their Applications
Volume135
DOIs
Publication statusPublished - May 2021

Keywords

  • math.ST
  • math.PR
  • stat.TH

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