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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
Main
Itovsn3 paclet
A Mathematica package for Symbolic Ito calculus
Ito Calculus
I
t
o
D
— Ito differential
I
t
o
I
n
t
e
g
r
a
l
— Ito integral of a stochastic differential expression
I
t
o
E
x
p
a
n
d
— simplify products of differentials
Semimartingales Properties
I
t
o
S
t
a
t
u
s
— report of current structures
G
e
t
I
t
o
P
r
o
c
— list of all defined semimartingales
I
n
i
t
i
a
l
V
a
l
u
e
▪
D
r
i
f
t
Create Semimartingales
I
t
o
I
n
i
t
— initialize all structures
I
t
o
R
e
s
e
t
— reset all structures
B
r
o
w
n
S
i
n
g
l
e
— create a single Brownian motion
B
r
o
w
n
B
a
s
i
s
— create many independent Brownian motions
I
t
o
s
d
e
— introduce semimartingales by the stochastic differential equations they satisfy
A
d
d
D
r
i
f
t
▪
A
d
d
F
i
x
e
d
▪
A
d
d
Q
u
a
d
V
a
r
▪
I
n
t
r
o
d
u
c
e
Placeholders
B
r
k
t
b
y
d
t
— placeholder for the formal quotient by
d
t
of a bracket differential
D
r
f
t
b
y
d
t
— placeholder for the formal quotient by
d
t
of the drift of a stochastic differential
F
i
x
e
d
— placeholder for value at initial time
Randomness Tests
R
a
n
d
o
m
Q
— tests whether an expression is a semimartingale or a stochastic differential
B
S
D
Q
— tests whether expression is a stochastic differential
T
e
c
h
N
o
t
e
s
▪
S
t
o
c
h
a
s
t
i
c
I
n
t
e
g
r
a
t
i
o
n
▪
B
e
s
s
e
l
p
r
o
c
e
s
s
e
s
▪
D
e
r
i
v
a
t
i
o
n
o
f
t
h
e
B
l
a
c
k
-
S
c
h
o
l
e
s
f
o
r
m
u
l
a
▪
D
i
s
t
r
i
b
u
t
i
o
n
o
f
t
h
e
L
e
v
y
s
t
o
c
h
a
s
t
i
c
a
r
e
a
▪
M
a
r
d
i
a
-
D
r
y
d
e
n
d
i
s
t
r
i
b
u
t
i
o
n
▪
C
o
u
p
l
e
d
p
a
i
r
s
o
f
B
r
o
w
n
i
a
n
m
o
t
i
o
n
s
r
e
f
l
e
c
t
i
n
g
o
f
f
a
h
a
l
f
-
p
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