Review of Stochastic Processes
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Last updated 1:23 PM on 11/23/22
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6 Terms
1
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Ito Process
dx = a(x,t)dt + b(x,t)dz
2
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Generalised Weiner Process (cont.)
dx = adt + bdz
3
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Generalised Weiner Process (disc.)
Δ x = aΔt + bΔz
= aΔt + ε*sqrt(Δt)
= aΔt + ε*sqrt(Δt)
4
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Weiner Process
Δz = z(T) -z(0)
Δz = ε*√(∆t), ε~ N(0,1)
E[∆z] = 0, σ²[∆z] = T
Δz = ε*√(∆t), ε~ N(0,1)
E[∆z] = 0, σ²[∆z] = T
5
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Markov Process
Past events give no information about future events
6
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Geometric Brownian motion (disc. and cont.)
dS = µSdt + σSdz
∆S = µS∆t + σSε√
∆S = µS∆t + σSε√