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I am a PhD student at UCL


Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious
Jul
22
revised Weak convergence of a collection of random variables starting from a random index
added 4 characters in body
Jul
22
revised Weak convergence of a collection of random variables starting from a random index
deleted 84 characters in body
Jul
22
asked Weak convergence of a collection of random variables starting from a random index
Jul
11
awarded  Yearling
Nov
29
revised Finding an example of a discrete-time strict local martingale.
deleted 47 characters in body; edited title
Nov
29
accepted Finding an example of a discrete-time strict local martingale.
Jul
11
awarded  Yearling
Jun
30
accepted Applying Ito to semi-group of Brownian motion in $\mathbb{R}^d$
Jun
8
awarded  Caucus
May
21
comment Limit of Wiener processes
Thank you, I just copy-pasted the latex.
May
21
comment Limit of Wiener processes
My notes say that Stratonovich would be $$\displaystyle \lim_{n->\infty}\sum_{k=0}^{[2^n t]-1}\big(\frac{W_{(k+1)2^{-n}}+W_{k2^{-n}}}{2}\big)(W_{(k+1)2^{-n}}-W_{k2^{-n}}‌​),$$ what am I missing?
May
21
comment Limit of Wiener processes
Central limit theorem won't help, central limit theorem is for a different type of convergence.
May
20
asked Applying Ito to semi-group of Brownian motion in $\mathbb{R}^d$
May
18
comment Are hitting times of Brownian motion independent?
if $c=\mathbb{P}(T_b<T_a)$, then, by OST, $0=\mathbb{E}[B_{T_a\wedge T_b}]=a(1-c)+bc$. Solve for $c$.
May
18
comment Hitting time of Brownian Motion with a drift
@mike, What is Wald? I have managed to use OST on the exponential martingale and then just differentiate the answer with respect to $b$ to compute the expression 1).
May
18
revised Hitting time of Brownian Motion with a drift
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May
18
comment Hitting time of Brownian Motion with a drift
Well OK it's easy to say $T<\infty$ $\mathbb{Q}$-a.s. by the properties of BM, hence it's a.s. finite under $\mathbb{P}$ (absolute continuity). So that is not a problem anymore.
May
18
asked Hitting time of Brownian Motion with a drift