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Finite dimensional filters for nonlinear stochastic difference equations with multiplicative noises

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  • Ferrante, Marco
  • Vidoni, Paolo

Abstract

We consider the filtering problem for partially observable stochastic processes solutions to systems of stochastic difference equations. In the first part of the paper we shall present a simple constructive method to obtain finite dimensional filters in discrete time. Then, applying some well-known results, mainly on the product of independent positive random variables, we shall present new finite dimensional filters and interpret some known results in a more general setting.

Suggested Citation

  • Ferrante, Marco & Vidoni, Paolo, 1998. "Finite dimensional filters for nonlinear stochastic difference equations with multiplicative noises," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 69-81, September.
    • Handle: RePEc:eee:spapps:v:77:y:1998:i:1:p:69-81
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    References listed on IDEAS

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    1. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
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    Cited by:

    1. Ferrante, Marco & Vidoni, Paolo, 1999. "A Gaussian-generalized inverse Gaussian finite-dimensional filter," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 165-176, November.
    2. Kon Kam King, Guillaume & Pandolfi, Andrea & Piretto, Marco & Ruggiero, Matteo, 2024. "Approximate filtering via discrete dual processes," Stochastic Processes and their Applications, Elsevier, vol. 168(C).
    3. de Pinho, Frank M. & Franco, Glaura C. & Silva, Ralph S., 2016. "Modeling volatility using state space models with heavy tailed distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 108-127.
    4. Chaleyat-Maurel, Mireille & Genon-Catalot, Valentine, 2006. "Computable infinite-dimensional filters with applications to discretized diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1447-1467, October.
    5. T. R. Santos, 2018. "A Bayesian GED-Gamma stochastic volatility model for return data: a marginal likelihood approach," Papers 1809.01489, arXiv.org.
    6. Ferrante, Marco & Frigo, Nadia, 2009. "Particle filtering approximations for a Gaussian-generalized inverse Gaussian model," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 442-449, February.

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