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 Nov10 comment Integration of Wiener process: $\int_{t_1}^{t_2} dB(s)$ @sos440 Is your identity true even for $\displaystyle \ \ \int_a^b \mathscr{\epsilon}(s)dB(s)$? (I don't know how to make that funny symbol you made). Nov10 accepted Breaking up Wiener processes with indicator functions? Nov10 comment Linear regression where undershooting isn't as bad as overshooting stats.stackexchange.com would be much more familiar with this literature. Nov10 comment Solving SDE: $dX(t) = udt + \sigma X(t)dB(t)$ @mike That makes complete sense. But, are you 100% sure this is accurate in this instance? Nov10 asked Integration of Wiener process: $\int_{t_1}^{t_2} dB(s)$ Nov9 revised Probability of passing through 3 specific nodes along a binomial tree deleted 81 characters in body Nov9 asked Solving SDE: $dX(t) = udt + \sigma X(t)dB(t)$ Nov9 accepted Derive an SDE for $B^2(t)$, where $B(t)$ is standard Brownian Motion Nov9 accepted Integrating $d(e^{-ut}X(t))$, where $X(t)$ is stochastic. Nov9 asked Integrating $d(e^{-ut}X(t))$, where $X(t)$ is stochastic. Nov9 asked Derive an SDE for $B^2(t)$, where $B(t)$ is standard Brownian Motion Nov9 comment Finite p-th variation implies zero-valued q-th variation. @did Thanks. Do you have any tips on how to progress furtheR? Nov9 revised Finite p-th variation implies zero-valued q-th variation. added 485 characters in body Nov9 asked Finite p-th variation implies zero-valued q-th variation. Nov9 comment Demonstrate that every martingale is a local martingale. @StefanHansen I think I don't understand what you mean by "one particular" sequence $(\sigma_n)_{n \in \mathbb{N}}$. Guessing what you mean; we can specify that each $\sigma_n = \text{inf}\{t \geq 0 : X_t = n\}$ where $X_{min(t,\sigma_n)}$ is the stopped process. However I can't see how this can help me solve the problem. Nov9 comment Why is $\operatorname{sign} B_t$ a predictable process? What is the notation $(t,\omega)\mapsto X_t(\omega)$? Nov9 awarded Critic Nov8 comment Demonstrate that every martingale is a local martingale. @StefanHansen Could you please dumb down your criticism of my attempt? I wikipedia'd localization but couldn't relate it to what you're saying. Nov8 comment Breaking up Wiener processes with indicator functions? Okay, so can I confirm that this is the correct argument: (i)$W_t(\omega) = {1}_{\{W_t(\omega) \geq 0\}}W_t(\omega) + {1}_{\{W_t(\omega) < 0\}}W_t(\omega)$ holds for each $\omega \in \Omega$. (ii)Therefore, $W_t = {1}_{\{W_t \geq 0\}}W_t + {1}_{\{W_t < 0\}}W_t$ is true (almost surely). Nov8 comment Breaking up Wiener processes with indicator functions? Okay, so you're suggesting that I use the fact that the identities I've stated hold path-wise (i.e. $\text{P-a.s.}$ under filtration equipped probability space with measure $P$), and therefore hold in all possible states of the world, and therefore the expressions are correct as they're stated.