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seen Feb 27 at 16:15

The earth is round (p < 0.01).


Nov
10
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).
Nov
10
accepted Breaking up Wiener processes with indicator functions?
Nov
10
comment Linear regression where undershooting isn't as bad as overshooting
stats.stackexchange.com would be much more familiar with this literature.
Nov
10
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?
Nov
10
asked Integration of Wiener process: $\int_{t_1}^{t_2} dB(s)$
Nov
9
revised Probability of passing through 3 specific nodes along a binomial tree
deleted 81 characters in body
Nov
9
asked Solving SDE: $dX(t) = udt + \sigma X(t)dB(t)$
Nov
9
accepted Derive an SDE for $B^2(t)$, where $B(t)$ is standard Brownian Motion
Nov
9
accepted Integrating $d(e^{-ut}X(t))$, where $X(t)$ is stochastic.
Nov
9
asked Integrating $d(e^{-ut}X(t))$, where $X(t)$ is stochastic.
Nov
9
asked Derive an SDE for $B^2(t)$, where $B(t)$ is standard Brownian Motion
Nov
9
comment Finite p-th variation implies zero-valued q-th variation.
@did Thanks. Do you have any tips on how to progress furtheR?
Nov
9
revised Finite p-th variation implies zero-valued q-th variation.
added 485 characters in body
Nov
9
asked Finite p-th variation implies zero-valued q-th variation.
Nov
9
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.
Nov
9
comment Why is $ \operatorname{sign} B_t $ a predictable process?
What is the notation $(t,\omega)\mapsto X_t(\omega)$?
Nov
9
awarded  Critic
Nov
8
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.
Nov
8
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).
Nov
8
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.