2
votes
1answer
86 views

Limit of a stochastic integral

Let $W_t$ be a one-dimensional Brownian motion and I would like to prove $$\lim_{\beta\rightarrow+\infty}\sup_{0\leq t\leq T}\left|e^{-\beta t} \int_0^te^{\beta s}\mathrm dW_s\right|=0$$ This is an ...
2
votes
1answer
473 views

Stochastic Calc

(a) Consider the process $$ \mathrm d\sqrt{v} = (\alpha - \beta\sqrt{v})\mathrm dt + \delta \mathrm dW $$ Here $\alpha, \beta,$ and $\delta$ are constants. Using Ito's Lemma show that $$ \mathrm dv = ...
0
votes
0answers
197 views

Exercises for “Limit Theorems for stochastic processes”

I am reading the book of Jacod and Shiryaev: Limit Theorems for Stochastic Processes. But there are no exercises in this book. Does anyone know a good source with exercises?