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## Special Topics in Economics

by: Ilene Heathcote

60

0

1

# Special Topics in Economics ECN 510

Marketplace > Syracuse University > Economcs > ECN 510 > Special Topics in Economics
Ilene Heathcote
Syracuse
GPA 3.98

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
1
WORDS
KARMA
25 ?

## Popular in Economcs

This 1 page Class Notes was uploaded by Ilene Heathcote on Wednesday October 21, 2015. The Class Notes belongs to ECN 510 at Syracuse University taught by Staff in Fall. Since its upload, it has received 60 views. For similar materials see /class/225650/ecn-510-syracuse-university in Economcs at Syracuse University.

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Date Created: 10/21/15
Note that if we would have taken t t7 instead ofti l then a different result would obtain 2 B1Bm B11771 1 l BtziliBlr Btbl 1 21 B39 tt 5 0 r twlr t 2 t BEH This shows that the integral 35st does not exist in RiemannStieltjes sense it matters how we choose t E tz1tl The limit is of a stochastic type and does not exist pathwise Note An important difference between t and t is that the former is a martingale whereas the latter is not This martingale property comes from taking tf 2 t71 ie at the beginning of the interval n1 ti over which we calculate the increments AiB This implies iBlt Bf1liiftlil BtrmlBh Bmllfm 0 l Construction of the It Integral We start by de ning a simple process Cf on 0 T Consider a partition 0 to lt lt tn T as usual and let 2 be a sequence of random variables such that Z is a function of B8 3 3 75141 ie adapted to ftiil 0BS7 3 g 7524 Also assume lt 00 Then de ne Ct Z finishN02 QM va i1 or in other words Zr tia1Stltt13 Cf Zn if t T Then we de ne T H 09st I Z 015121 Bit Btzil 0 711 iZlAZB ZAB i1 Note that this is a random variable We can extend this de nition to a stochastic process by letting the endpoint t of the integral vary from 0 to T

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