\begin{thebibliography}{14}
\providecommand{\natexlab}[1]{#1}
\providecommand{\url}[1]{\texttt{#1}}
\expandafter\ifx\csname urlstyle\endcsname\relax
  \providecommand{\doi}[1]{doi: #1}\else
  \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi

\bibitem[Amari(1998)]{Amari1998}
Shun-Ichi Amari.
\newblock Natural gradient works efficiently in learning.
\newblock \emph{Neural Computation}, 10:\penalty0 251--276, 1998.

\bibitem[Ambrosio et~al.(2005)Ambrosio, Gigli, and Savare]{Ambrosio2005}
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savare.
\newblock Gradient flows in metric spaces and in the space of probability
  measures.
\newblock \emph{Lectures in Mathematics. ETH Z{\"u}rich}, 2005.

\bibitem[Brigo(1997)]{Brigo97}
Damiano Brigo.
\newblock On nonlinear {SDE}'s whose densities evolve in a finite--dimensional
  family.
\newblock volume~23, pages 11--19. Birkh\"auser, 1997.

\bibitem[Brigo et~al.(1999)Brigo, Hanzon, and Gland]{Brigo99}
Damiano Brigo, Bernard Hanzon, and Fran{\c c}ois Gland.
\newblock Approximate nonlinear filtering by projection on exponential
  manifolds of densities.
\newblock \emph{Bernoulli}, 5, 1999.

\bibitem[Bures(1969)]{Bures69}
Donald Bures.
\newblock An extension of {K}akutani's theorem on infinite product measures to
  the tensor product of semifinite {$w^{\ast} $}-algebras.
\newblock \emph{Transactions of the American Mathematical Society},
  135:\penalty0 199--212, 1969.

\bibitem[Halder and Georgiou(2017)]{Halder2017}
Abhishek Halder and Tryphon Georgiou.
\newblock \emph{Gradient flows in uncertainty propagation and filtering of
  linear Gaussian systems}.
\newblock 2017.

\bibitem[Halder and Georgiou(2018)]{Halder2018}
Abhishek Halder and Tryphon Georgiou.
\newblock \emph{Gradient flows in filtering and {F}isher-{R}ao geometry}.
\newblock Annual American Control Conference, 2018.

\bibitem[Hanzon and Hut(1991)]{Hanzon1991}
Bernard Hanzon and R.~Hut.
\newblock New results on the projection filter.
\newblock \emph{Serie Research Memoranda 0023}, 1, 1991.

\bibitem[Jordan et~al.(1998)Jordan, Kinderlehrer, and Otto]{Jordan98}
Richard Jordan, David Kinderlehrer, and Felix Otto.
\newblock The variational formulation of the {F}okker--{P}lanck equation.
\newblock \emph{SIAM Journal on Mathematical Analysis}, 29:\penalty0 1--17,
  1998.

\bibitem[Kushner(1967)]{Kushner1967}
H.~Kushner.
\newblock Approximations to optimal nonlinear filters.
\newblock \emph{IEEE Transactions on Automatic Control}, 12\penalty0
  (5):\penalty0 546--556, 1967.

\bibitem[Lambert et~al.(2022{\natexlab{a}})Lambert, Bonnabel, and
  Bach]{Lambert22a}
Marc Lambert, Silv{\`e}re Bonnabel, and Francis Bach.
\newblock The recursive variational {G}aussian approximation ({R-VGA}).
\newblock \emph{Statistics and Computing}, 32\penalty0 (1), 2022{\natexlab{a}}.

\bibitem[Lambert et~al.(2022{\natexlab{b}})Lambert, Bonnabel, and
  Bach]{Lambert22b}
Marc Lambert, Silv{\`e}re Bonnabel, and Francis Bach.
\newblock {The continuous-discrete variational {K}alman filter (CD-VKF)}.
\newblock In \emph{Conference on Decision and Control}, 2022{\natexlab{b}}.

\bibitem[Lambert et~al.(2022{\natexlab{c}})Lambert, Chewi, Bach, Bonnabel, and
  Rigollet]{Lambert22c}
Marc Lambert, Sinho Chewi, Francis Bach, Silv{\`e}re Bonnabel, and Philippe
  Rigollet.
\newblock Variational inference via {W}asserstein gradient flows.
\newblock In \emph{Advances in Neural Information Processing Systems},
  2022{\natexlab{c}}.

\bibitem[Laugesen et~al.(2014)Laugesen, Mehta, Meyn, and
  Raginsky]{Laugesen2014}
R.~Laugesen, P.~G. Mehta, S.~P. Meyn, and M.~Raginsky.
\newblock Poisson's equation in nonlinear filtering.
\newblock In \emph{Conference on Decision and Control}, pages 4185--4190, 2014.

\end{thebibliography}
