How does one integrate a Brownian motion. Stochastic Process

1. BROWNIAN MOTION ITO’S
CALCULUS
by Karthikeya Subramanian
under the guidance of Dr.M. Sivakumar

2. Brownian Motion
A real-valued stochastic process W(·) is called a Brownian motion or Wiener
process :
W(0) = 0
W(t) − W(s) is N(0, t − s) for all t ≥ s ≥ 0
for all times 0 < t1 < t2 < ··· < tn the random variables
W(t1), W(t2) − W(t1),...,W(tn) − W(tn−1) are independent (“independent
increments”).

3. Stochastic Differential Equations
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