We are interested in the effects of fluctuation which are observed
in biological phenomena. There is a big variety in the appearance
of the effects, however many of mathematical descriptions have
much similarity. The most elemental and basic fluctuoation can be
realized by white noise, either Gaussian or compound Poisson type.
This fact leads us to discuss functions of white noise, call them
white noise functionals of either Gaussian or Poisson type, which
may well describe biological systems mathematically. We then consider
the analysis of those functionals. The analysis in question will be
the causal calculus, since the biological phenomena are to be
evolutional in many cases, that is, they are developing as
the time goes by.
To be more concrete, some of the following topics in mathematical
biology will be discussed.\par
1) Applications of the Wiener expansion and of the Hellinger-Hahn
theory, \par
2) Construction of innovations of biological, evolutional phenomena
with fluctuation. It is often helped by a method of using the
infinite dimensional rotation group, \par
3) Creation and annihilation operators applied to random evolutional
phenomena, irreversibility and other properties,\par
4) Genralizations of the Lotka-Volterra equation with fluctuation.
5) Functionals of Poisson noise with application to biology.
6) Others.