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![Page 1: INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive the htb equation we needed taylor expansions chain rule we recap the same for stochastic](https://reader030.vdocument.in/reader030/viewer/2022040614/5f0b82147e708231d430dd40/html5/thumbnails/1.jpg)
9 STOCHASTICINTEGRATIONRECEP
![Page 2: INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive the htb equation we needed taylor expansions chain rule we recap the same for stochastic](https://reader030.vdocument.in/reader030/viewer/2022040614/5f0b82147e708231d430dd40/html5/thumbnails/2.jpg)
TO DERIVE THE HTB EQUATION WE NEEDED
TAYLOR EXPANSIONSCHAIN RULE
WE RECAP THE SAME FOR STOCHASTIC INTEGRAL
![Page 3: INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive the htb equation we needed taylor expansions chain rule we recap the same for stochastic](https://reader030.vdocument.in/reader030/viewer/2022040614/5f0b82147e708231d430dd40/html5/thumbnails/3.jpg)
STOCHASTICINTEGRAL INDEPENDENTGAUSSIANINCREMENTS LINEvariation
FOR BROWNIAN MOTION sewor
SO STOCHASTIC
INTEGRAL
![Page 4: INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive the htb equation we needed taylor expansions chain rule we recap the same for stochastic](https://reader030.vdocument.in/reader030/viewer/2022040614/5f0b82147e708231d430dd40/html5/thumbnails/4.jpg)
STOCHASTICDIFFERENTIAL EQUATIONS
DEFINE
LET 8 so
THIS GIVES US TAYLOR APPROXIMATIONS FOR 5D Es
![Page 5: INTEGRATION - appliedprobability.files.wordpress.com · 9 stochastic integration recep. to derive the htb equation we needed taylor expansions chain rule we recap the same for stochastic](https://reader030.vdocument.in/reader030/viewer/2022040614/5f0b82147e708231d430dd40/html5/thumbnails/5.jpg)
ITISFOR MULA For OUR SDE FROM BEFORE
THIS GIVES US A CHAINRULE FOR S D E s