INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive...
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9 STOCHASTIC INTEGRATION RECEP
Transcript of INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive...
9 STOCHASTICINTEGRATIONRECEP
TO DERIVE THE HTB EQUATION WE NEEDED
TAYLOR EXPANSIONSCHAIN RULE
WE RECAP THE SAME FOR STOCHASTIC INTEGRAL
STOCHASTICINTEGRAL INDEPENDENTGAUSSIANINCREMENTS LINEvariation
FOR BROWNIAN MOTION sewor
SO STOCHASTIC
INTEGRAL
STOCHASTICDIFFERENTIAL EQUATIONS
DEFINE
LET 8 so
THIS GIVES US TAYLOR APPROXIMATIONS FOR 5D Es
ITISFOR MULA For OUR SDE FROM BEFORE
THIS GIVES US A CHAINRULE FOR S D E s