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Wolfram Language
Itovsn3
Guides
Main
Tech Notes
Bessel
BlackScholes
ItoArea
MardiaDryden
Reflect
Stochastic Integration
Symbols
AddDrift
AddFixed
AddQuadVar
Brktbydt
BrownBasis
BrownSingle
BSDQ
Drftbydt
Drift
Fixed
GetItoProc
InitialValue
Introduce
ItoD
ItoExpand
ItoInit
ItoIntegral
ItoReset
Itosde
ItoStatus
RandomQ
FernandoDuarte`Itovsn3`
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Examples
(
4
)
Basic Examples
(
1
)
Initialize:
I
n
[
1
]
:
=
I
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o
R
e
s
e
t
[
t
,
d
t
]
O
u
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[
1
]
/
/
T
a
b
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F
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m
=
I
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s
n
3
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.
.
.
I
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3
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d
t
Introduce two independent Brownian motions:
I
n
[
2
]
:
=
B
r
o
w
n
B
a
s
i
s
[
{
X
,
Y
}
,
{
1
,
0
}
]
The simplest view of the Ito integral is that it is the right-inverse of the stochastic differential:
I
n
[
3
]
:
=
I
t
o
D
I
t
o
I
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e
g
r
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[
Y
d
X
]
d
X
Y
O
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t
[
3
]
=
T
r
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e
I
t
o
I
n
t
e
g
r
a
l
knows the very simplest facts about Ito integrals:
I
n
[
4
]
:
=
I
t
o
I
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g
r
a
l
[
d
X
]
O
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t
[
4
]
=
-
1
+
X
S
c
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p
e
(
1
)
G
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s
&
E
x
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(
1
)
N
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a
t
E
x
a
m
p
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e
s
(
1
)
S
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A
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