Bernard Hanzon
Encyclopedia
Bernand Hanzon is an academic, mathematician
, and researcher
. He has worked on systems theory
, probability
and statistics
, and mathematical finance
. He is best known for a number of results in these areas.
and Francois Le Gland. The Projection filters are a family of approximate nonlinear filters based on the differential geometry approach to statistics, also related to information geometry
. This has been a contribution to approximate solutions to the filtering problem (stochastic processes)
, that has been applied to optics by van Handel and Mabuchi (2005). It has also been considered by the Swedish Defense Research Agency in Berefelt, Hamberg and Robinson (2003), and cited in the context of GPS and navigation in connection with the use of the exponential family
for the approximated nonlinear filter in Azimi-Sadjadi and Krishnaprasad (2005). Hanzon, with Brigo, has also explored the possible use of Filtering techniques in Mathematical Finance (1998).
as a PhD student of Hanzon and Jan van Schuppen.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, and researcher
Researcher
A researcher is somebody who performs research, the search for knowledge or in general any systematic investigation to establish facts. Researchers can work in academic, industrial, government, or private institutions.-Examples of research institutions:...
. He has worked on systems theory
Systems theory
Systems theory is the transdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research...
, probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, and mathematical finance
Mathematical finance
Mathematical finance is a field of applied mathematics, concerned with financial markets. The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will derive and extend the mathematical...
. He is best known for a number of results in these areas.
Nonlinear filtering: Projection filters
Hanzon introduced the idea of Projection Filter in Hanzon (1987) and Hanzon and Hut (1991), then fully developed and formalized with the help of Damiano BrigoDamiano Brigo
Damiano Brigo is an applied mathematician, and current Gilbart Chair of Financial Mathematics at King's College, London, known for a number of results in systems theory, probability and mathematical finance.-Main results:...
and Francois Le Gland. The Projection filters are a family of approximate nonlinear filters based on the differential geometry approach to statistics, also related to information geometry
Information geometry
Information geometry is a branch of mathematics that applies the techniques of differential geometry to the field of probability theory. It derives its name from the fact that the Fisher information is used as the Riemannian metric when considering the geometry of probability distribution families...
. This has been a contribution to approximate solutions to the filtering problem (stochastic processes)
Filtering problem (stochastic processes)
In the theory of stochastic processes, the filtering problem is a mathematical model for a number of filtering problems in signal processing and the like. The general idea is to form some kind of "best estimate" for the true value of some system, given only some observations of that system...
, that has been applied to optics by van Handel and Mabuchi (2005). It has also been considered by the Swedish Defense Research Agency in Berefelt, Hamberg and Robinson (2003), and cited in the context of GPS and navigation in connection with the use of the exponential family
Exponential family
In probability and statistics, an exponential family is an important class of probability distributions sharing a certain form, specified below. This special form is chosen for mathematical convenience, on account of some useful algebraic properties, as well as for generality, as exponential...
for the approximated nonlinear filter in Azimi-Sadjadi and Krishnaprasad (2005). Hanzon, with Brigo, has also explored the possible use of Filtering techniques in Mathematical Finance (1998).
Current and past affiliations
Hanzon is currently Associate Professor of Mathematical Finance at the University College Cork, College of Science, Engineering and Food Science, School of Mathematical Sciences, Cork, Ireland. His current interests include mathematical finance and algebraic methods in systems theory. Prior to that Hanzon had been an assistant professor at the Free University of Amsterdam. Hanzon holds a PhD in Systems Theory.Notable students
The Mathematics genealogy project lists Damiano BrigoDamiano Brigo
Damiano Brigo is an applied mathematician, and current Gilbart Chair of Financial Mathematics at King's College, London, known for a number of results in systems theory, probability and mathematical finance.-Main results:...
as a PhD student of Hanzon and Jan van Schuppen.
External links
- Bernard Hanzon at the Math genealogy project