41 reputation
12
bio website
location
age
visits member for 1 year, 11 months
seen Feb 27 at 16:15

The earth is round (p < 0.01).


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.
Nov
8
asked Demonstrate that every martingale is a local martingale.
Nov
8
awarded  Commentator
Nov
8
comment Breaking up Wiener processes with indicator functions?
So this confirms the two identifies path-wise. (i.e. for $W_t(\omega)$ and $|W_t(\omega)|$). However, I'm not quite sure how this can then be extended to demonstrate the case for the full $W_t$ random variable?