MATLAB Wiener Prozess

Question 1

generate a matrix of increments from N(0,1)

Answer 1

dw = (1/sqrt(m))*randn(m,n)

Question 2

add zeros as the first row

Answer 2

wiener_process = cumsum([zeros(1,n);dw])

Question 3

drop the last observation

Answer 3

wiener_process = wiener_process(1:(length(wiener_process)-1),:)

Question 4

generate time

Answer 4

t = 0:1/m:(1-1/m)
tmat = repmat(t',1,n)

Question 5

generate quadratic variation

Answer 5

quadratic_variation = cumsum(dw.*dw)

Question 6

stochastic integral 2wdw

Answer 6

stochastic_integral_1 = cumsum(wiener_process.*dw)

Question 7

stochastic process w^2-t

Answer 7

wiener_process_martingale = wiener_process.^2-tmat