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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
FernandoDuarte`Itovsn3`
Itosde
​
Itosde
[X,dXsd,
X
0
]
introduces and sets up a basic semimartingale identifier
X
with basic stochastic differential identifier
dX
and initial value expression
X
0
, and satisfying the second- and first-order structure implied by the stochastic differential equation
dXsd
.
​
Examples  
(1)
Basic Examples  
(1)
Initialize:
In[1]:=
ItoInit
[t,dt]
Out[1]//TableForm=
Itovsn3 initialized
with time semimartingale t
and time differential dt
Create a Brownian motion:
In[2]:=
BrownSingle
[B,0]
Out[2]=
0
Create a semimartingale
X
:
In[3]:=
Itosde
[X,dXμdt+σdB,X0]
Structure reflects
dX
and
dB
, including their quadratic co-variation:
In[4]:=
ItoStatus
[]
Out[4]=
Summary of current structure of stochastic differentials
Current second-order structure of semimartingale differentials:
dX
dB
dt
dX
dt
2
σ
dtσ
0
dB
dtσ
dt
0
dt
0
0
0
Current first-order structure of semimartingale differentials:
dX
dB
dt
dtμ
0
dt
Current initial values:
X
B
t
X0
0
0
SeeAlso
AddDrift
 
▪
AddQuadVar
 
▪
BrownBasis
 
▪
BrownSingle
 
▪
Introduce
RelatedGuides
▪
Main
""

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