| My research interests include:
filtering theory, Markov processes, stochastic convergence, limit
theorems, particle systems, stochastic analysis, and applications to
mathematical finance, communication networks, and industrial problems.
The following simple example will
illustrate application of some of these interests:
A person watching the planes above a
busy airport does not know how many aircraft there are without counting
them nor does he/she know the exact positions of the planes. However,
he/she is sure that they will interact to avoid collisions and close
calls. Hence, this "unknown number" of planes might collectively be
labelled an "interacting random system". A consideration of local
weather variations between the ground and each craft, the effect of a
craft's wake on the other planes, and additional subtle factors would
lead the astute observer to conclude that the planes are operating in
an unknown or "random environment".
The features mentioned in the above
air traffic management example are also common to other interacting
random systems like air and fluid flow, traffic in communication
networks, surveillance of submarines, chemical reactions, and stock
price fluctuations. Moreover, some of these examples also exhibit "long
(time) memory" meaning that it is impossible to isolate future
happenings from the distant past. Such properties severely complicate
the modeling, model robustness studies, and prediction procedures for
our interacting random systems and often render established methods
inappropriate. We establish new model classes and study their
qualitative and robustness properties. Secondly, we are interested in
strategies for predicting the future state, e.g. wind prediction or
aircraft position, of our interacting random systems.
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