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doi:10.1090/bull/2014-51-04

Bull. Amer. Math. Soc.

2014

DOI: 10.1090/bull/2014-51-04

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Abstract: Abstract. We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge-Ampère type equations arising in that context.

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A baker’s dozen of new particle flows for nonlinear filters, Bayesian decisions and transport

Daum

Huang

2015

SPIE Proceedings

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We describe a baker's dozen of new particle flows to compute Bayes' rule for nonlinear filters, Bayesian decisions and learning as well as transport. Several of these new flows were inspired by transport theory, but others were inspired by physics or statistics or Markov chain Monte Carlo methods.Keywords-particle filter, nonlinear filter, particle flow, transport problem, extended Kalman filter, MongeKantorovich optimal transport I. Signal Processing, Sensor/Information Fusion, and Target Recognition XXIV, edited by Ivan Kadar, Proc. of SPIE Vol. 9474, 94740J · © 2015 SPIE CCC code: 0277-786X/15/$18 · Downloaded From: http://proceedings.spiedigitallibrary.org/ on 09/30/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Proc. of SPIE Vol. 9474 94740J-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 09/30/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Proc. of SPIE Vol. 9474 94740J-3 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 09/30/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Proc. of SPIE Vol. 9474 94740J-12 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 09/30/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

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A baker’s dozen of new particle flows for nonlinear filters, Bayesian decisions and transport

Daum

Huang

2015

SPIE Proceedings

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Untitled

Abstract: Abstract. We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge-Ampère type equations arising in that context.

Cited by 1 publication

References 63 publications

A baker’s dozen of new particle flows for nonlinear filters, Bayesian decisions and transport

A baker’s dozen of new particle flows for nonlinear filters, Bayesian decisions and transport

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