
138 High Performance Programming for Soft Computing
energy exchanges are not included in the description). We also state that,
as T tends to unit, R tends to zero and the following ratio has a defi nite
value in the limit:
ோ
ఛ
ൌ
ଵ
ଶఏ
ൌߣ.
(6.3.3)
Here θ will be denoted as the characteristic time. In addition c
2
θ = D
will be stated as the diffusion coeffi cient of the process, so:
߲ܲ
ଵ
߲ݐ
ൌെܿ
߲ܲ
ଵ
߲ݔ
ͳ
ʹߠ
ܲ
ଶ
െ
ͳ
ʹߠ
ܲ
ଵ
߲ܲ
ଶ
߲ݐ
ൌെܿ
߲ܲ
ଶ
߲ݔ
ͳ
ʹߠ
ܲ
ଵ
െ
ͳ
ʹߠ
ܲ
ଶ
ൢ
(6.3.4)
On the other hand, we can require from the process the following
conditions as a consequence of taking the limit:
Ͳܲ
ଵ
ǡܲ
ଶ
ǡߩǡȁ
ȁͳ
ߩൌܲ
ଵ
ܲ
ଶ
ܬൌܲ
ଵ
െܲ
ଶ
න
ߩ
ሺ
ݔǡݐ
ሻ
݀ݔൌͳ
ஶ
௫ୀିஶ
ۙ
(6.3.5)
In other words, the description (6.3.4), with ...