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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
ItoD
— Ito differential
ItoIntegral
— Ito integral of a stochastic differential expression
ItoExpand
— simplify products of differentials
Semimartingales Properties
ItoStatus
— report of current structures
GetItoProc
— list of all defined semimartingales
InitialValue
▪
Drift
Create Semimartingales
ItoInit
— initialize all structures
ItoReset
— reset all structures
BrownSingle
— create a single Brownian motion
BrownBasis
— create many independent Brownian motions
Itosde
— introduce semimartingales by the stochastic differential equations they satisfy
AddDrift
▪
AddFixed
▪
AddQuadVar
▪
Introduce
Placeholders
Brktbydt
— placeholder for the formal quotient by
dt
of a bracket differential
Drftbydt
— placeholder for the formal quotient by
dt
of the drift of a stochastic differential
Fixed
— placeholder for value at initial time
Randomness Tests
RandomQ
— tests whether an expression is a semimartingale or a stochastic differential
BSDQ
— tests whether expression is a stochastic differential
TechNotes
▪
Stochastic Integration
▪
Bessel processes
▪
Derivation of the Black-Scholes formula
▪
Distribution of the Levy stochastic area
▪
Mardia-Dryden distribution
▪
Coupled pairs of Brownian motions reflecting off a half-plane
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