Is the nearest walk to Brownian motion approximately uniform?
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Let $W:[0,1]\rightarrow\mathbb R$ be standard Brownian motion with $W(0)=0$. Let $F_n$ denote the collection of all the $2^n$ many piecewise linear continuous functions $f:[0,1]\rightarrow\mathbb R$ such that $f(0)=0$ and $f$ is linear with slope $\pm \sqrt{n}$ on the intervals $[\frac in,\frac{i+1}n]$ for $0\le i<n$. Let $\psi_n$ denote a uniformly randomly chosen element of $F_n$, i.e., $\mathbb P(\psi_n=f)=2^{-n}$ for each $f\in F_n$. Let $\phi_n$ denote a uniformly randomly chosen element...
Answer:
My understanding of the question is this: There is a function $V_n$ that maps the $L^\infty([0,1])$...
Bjørn Kjos-Hanssen at Mathoverflow Mark as irrelevant Undo
Other solutions
Many Finance research articles model value of assets using Brownian motion e.g. Vassalou and Xing (2004, Default Risk in Equity Returns, JoF). I wonder who started using Brownian motion in Finance and why is it being used quite regularly. How is it difference...
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Louis Bachelier was the first to use Brownian motion to model securities in his 1900 thesis. Brownian...
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Answer:
He ran 5 mph faster than he walked. So if his walking speed is v, his running speed is v + 5. He ran...
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Part A: Motion with Uniform Velocity In the first part of this experiment, you will examine the motion of a ball moving in a straight line at a constant speed (i.e., no acceleration). To begin, find an open area in which the ball can roll smoothly on...
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is it a question or explanation of kinematics. Be brief with your question so that we can answer.
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E.g. Random walk brownian motion framework applied to financial options pricing, Bose-Einstein condensation models applied to network theory, etc.
Answer:
1) Concept of "Patter variables" by Talcott Parsons which have element of stress or strain...
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Background: I have one year (3 quarters at my school) to take any course I want. My long term goal is to be able to apply machine learning techniques effectively to business problems/ work in startups. My knowledge at the time of embarking on this...
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In my opinion the three classes you cannot pass up are Numerical Analysis, Linear Algebra and Advanced...
Robert Eckhardt at Quora Mark as irrelevant Undo
You can't choose your family. Now I know why. It is because if you could, people like Leo will be left to rot to death. Not that I’d complain. "Could you go any slower?” I said at last. "Hey, I am just trying to stick to the speed limit"...
Answer:
Well, I'd say it's good. I would usually appreciate more action, and more characterization. One way...
artemis at Yahoo! Answers Mark as irrelevant Undo
You can't choose your family. Now I know why. It is because if you could, people like Leo will be left to rot to death. Not that I’d complain. "Could you go any slower?” I said at last. "Hey, I am just trying to stick to the speed limit"...
Answer:
I would continue reading. I loved the interaction between Tessa and Leo. There's enough questions left...
artemis at Yahoo! Answers Mark as irrelevant Undo
You can't choose your family. Now I know why. It is because if you could, people like Leo will be left to rot to death. Not that I’d complain. "Could you go any slower?” I said at last. "Hey, I am just trying to stick to the speed limit"...
Answer:
My only critique is the first few sentences. They're kind of confusing, and they set the tone for a...
artemis at Yahoo! Answers Mark as irrelevant Undo
You can't choose your family. Now I know why. It is because if you could, people like Leo will be left to rot to death. Not that I’d complain. "Could you go any slower?” I said at last. "Hey, I am just trying to stick to the speed limit"...
Answer:
The plot line for me personally is quite engaging although some language choices could be improved....
artemis at Yahoo! Answers Mark as irrelevant Undo
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