Suppose that the continuous-time stochastic process X = (Xt) is defined as Xt = 1 2 t
Question:
Suppose that the continuous-time stochastic process X = (Xt) is defined as Xt = 1 2
t 0
λ2 s ds +
t 0
λs dzs, where z = (zt) is a one-dimensional standard Brownian motion and λ = (λt) is some ‘nice’
stochastic process.
(a) Argue that dXt = 1 2 λ2 t dt + λt dzt.
(b) Suppose that the continuous-time stochastic process ξ = (ξt) is defined as ξt =
exp{−Xt}. Show that dξt = −λtξt dzt.
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