Geography Reference
In-Depth Information
Fig. 12.6
RW simulation result with 500 time steps
12.3.1.2
Brownian Bridges Within Space-Time Prisms
We proceed to the continuous space and time and apply the technique of
Brownian
Bridges
(BBs). A Brownian Bridge is a continuous-time stochastic movement
between two known values, estimated at stationary increments. In economics and
finance, BBs has been applied to analyze stock market prices (Chow and et al.
1995
;
Lo
1991
; Rostek and Schöbel
2006
). In ecological research, the
Brownian Bridge
Movement Model
(BBMM) has been developed to estimate an animal's probability
of occurrence at a given geographic location and time (Brillinger et al.
2002
;Holmes
et al.
1994
; Horne et al.
2007
).
A BB in one dimension from
a
2
r
to
b
2
r
on [0,
T
]is:
W.t/
W.T/
;0
t
b
a
T
t
T
B.t/
a
!
b
D
a
C
t
T
(12.20)
where
f
W
t
g
is a standard Wiener process (a.k.a. Brownian motion) that is indexed
by nonnegative real numbers t, and should satisfy the following properties:
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