Stochastic Integral
2015-10-28 18:53:51 1 举报AI智能生成
随机积分学习大纲
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Riemann Integral
Riemann sum
Existence
(piecewise) continuous
Riemann-Stieltjes Integral
Riemann-Stieltjes sum
Existence
Discontinuity not at the same point
Bounded p/q-variation
1/p+1/q>1
Ito stochastic Integral
Motivation
Bt has bounded variation of p>2
Proof
P=2, variation goes to infinity
Converge in mean square
Show that
For simple process
Continuous sample paths
adapted to natural filtration of B
Martingale
Isometry
General process
Fact 1
Fact 2
Properties
FCLT for partial sum process
+continuous mapping theorem
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