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| bio | website | |
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| location | ||
| age | ||
| visits | member for | 10 months |
| seen | yesterday | |
| stats | profile views | 15 |
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Mar 12 |
comment |
Martingale inequality related to Kolmogorov's maximal inequality It looks like your question got overlooked. Somebody else asked the same question a couple of weeks ago. You can find my answer over there: math.stackexchange.com/questions/313415/… |
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Mar 5 |
awarded | Critic |
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Mar 5 |
comment |
Definition of Ito process Oh that's just the definition to take for $\mu_2$ to make your bullet points (1) and (2) be the same process. |
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Mar 5 |
comment |
Definition of Ito process I just realized the article I pointed you to is ridiculously lacking in content, my bad. Supposing your time domain is, say, $[0,T]$, both $\mu, \sigma$ are functions of the form $f : \Omega \times [0, T] \to \mathbb{R}$ such that $f(\cdot, t)$ is measurable by your filtration. Here $\Omega$ is your sample space. This allows for position dependence. If $\mu_1$ is as in your first bullet point, the $\mu_2$ in your second bullet point would be $\mu_2(\omega, t) := \mu_1(X_1(\omega), t)$. Does this help? Edit: by position I meant past/present value. |
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Mar 5 |
comment |
Definition of Ito process You're oversimplifying what you read in the Wiki article in your second bullet point. The formula you pasted is not quite the formula you can find in the article. If you look at the article carefully, it says that $\mu$, $\sigma$ are predictable processes, meaning they depend on time and position. en.wikipedia.org/wiki/Predictable_process |
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Mar 4 |
awarded | Informed |
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Mar 2 |
revised |
Martingale and bounded stopping time added 2 characters in body |
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Mar 2 |
answered | Martingale and bounded stopping time |
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Jan 7 |
comment |
Is the area of intersection of convex polygons always convex? You are welcome my friend. |
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Jan 3 |
revised |
Is the area of intersection of convex polygons always convex? describe algorithm to find maximal triangle + improved formatting |
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Jan 3 |
comment |
Is the area of intersection of convex polygons always convex? Thanks Sigur! Now I see what was going on with Rahul, I guess the OP also wanted a way to determine what the maximal triangle is. My apologies for missing that. You're right Sigur, I think maximizing among all pairs $(L, h_L)$ is the best way to do it, let me edit my post above to reflect your point. |
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Jan 3 |
comment |
Is the area of intersection of convex polygons always convex? This isn't getting us anywhere :-) If perhaps you think my original presentation is not clear, I will be happy to throw in more details to straighten it out. |
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Jan 3 |
comment |
Is the area of intersection of convex polygons always convex? Hi Rahul, I'm afraid I don't understand the point you're making. EDIT: To be clear, as you pointed out, this was not supposed to be a constructive method for global maxima (i.e. start with a triangle, wiggle it around, construct a global maximum). All it does is start with a triangle and make a triangle that is at least as good, and whose vertices are nice. So bootstrap it with a maximal triangle and voila. |
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Jan 3 |
answered | Is the area of intersection of convex polygons always convex? |
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Jan 3 |
awarded | Supporter |
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Jan 2 |
comment |
Easy but hard question regarding concave functions! Sure my friend, glad you liked it. |
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Dec 31 |
awarded | Editor |
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Dec 31 |
revised |
Easy but hard question regarding concave functions! corrected a detail that was glossed over |
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Dec 31 |
awarded | Teacher |
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Dec 31 |
answered | Easy but hard question regarding concave functions! |
