Brownian motion Definition and 84 Threads

Hi guys, It's been a while since high school, and now I'm faced with a problem I need to solve in a few days (attached). Would someone please help me through that? I would really appreciate support.

I need to answer these questions, but I don't have a clue what they mean. Could anybody shed some light? Find: (a) $E({B_1^4})$ (b) $E({B_1^6})$ (c) $E(e^{B_1})$ (e) $E({5B_1}^4+{6B_1}^2+{5B_1}^3)$ (e) $E(B_2 B_3)$ (f.) $E(e^{B_2+B_3})$

Hello, Given a Brownian Motion process B(t) for 0≤t≤T, we can write it more explicitly as B(t,ω) where ω\inΩ, where Ω is the underlying sample space. My question is: what is the cardinality of Ω. I.e. what is |Ω|? My thoughts are that it is an uncountable set, based on the observation...

Hi all, I feel like there's a missing link in my understanding of brownian motion. I'm comfortable with the "method of http://fraden.brandeis.edu/courses/phys39/simulations/Uhlenbeck%20Brownian%20Motion%20Rev%20Mod%20Phys%201945.pdf" where the signal is written as a Fourier series, and with...

http://xanadu.math.utah.edu/java/brownianmotion/1/ I can't imagine

Problem: Let M(t) = max X(s), 0<=s<=t Show that P{ M(t)>a | M(t)=X(t)} = exp[-a^2/(2t)] Attempt at solution: It seems this should equal P(|X(t)| > a), but evaluating the normal distribution from a to infinity cannot be expressed in closed form as seen in the solution (unless this is...

Problem: Let X(t), t>0 denote the birth and death process that is allowed to go negative and that has constant birth and death rates Ln = L, un = u (n is integer). Define u and c as functions of L in such a way that cX(t), t>u converges to Brownian motion as L approaches infinity. Attempt...

Let B_t be Brownian motion in \mathbb R beginning at zero. I am trying to find expressions for things like E[(B^n_s - B^n_t)^m] for m,n\in \mathbb N. So, for example, I'd like to know E[(B^2_s - B^2_t)^2] and E[(B_s - B_t)^4]. Here are the only things I know: E[B_t^{2k}] = \frac{(2k)!}{2^k...

Homework Statement Suppose B_t is a Brownian motion. I want to show that if you fix t_0 \geq 0, then the process W_t = B_{t_0+t} - B_{t_0} is also a Brownian motion.Homework Equations Apparently, a stochastic process X_t is a Brownian motion on \mathbb R^d beginning at x\in \mathbb R^d if it...

Let me start off by saying that I very well know that PM is impossible. Thermodynamics aren't just good ideas-they're the law. :) I have heard that Brownian Motion will go on infinitely, but you can't harness it and it is useless perpetual motion. Is this true?

Is there a theory regarding why particles move in random paths. My high school physics teacher said it's energy left over from the big bang, but that doesn't explain why they move in random paths, they could just as easily obey Newton's Laws of Motion and still have energy left over from the...

Dear list, Imagine a table of upper surface area S sitting in an open field, with nothing on it. We know that S is subjected to a downward atmospheric pressure P due to a cylindrical column of air of volume V extending vertically from S to the end of the terrestrial atmosphere. Assume this...

I watched a show on Fractals and it sort of remind me of Brownian motion. So my question is has anyone ever used fractals to explain Brownian motion?

for a brownian motion W(t) W(t_i+1)-W(t_i) is normal distribution with mean 0 and variance t_i+1-t_i so this means var(W(t_i+1)-W(t_i))=var(W(t_i+1))-var(W(t_i))=t_i+1-t_i I don't think the above equation satisfies because W(t_i+1) and W(t_i) are not independent. Any comment? thanks

Hi: I want to know the quadratic covariation of Brownian motion B(t) and poisson process N(t).Is it B(t)? Thanks !

Using Brownian Motion to solve for 4 things PLZ HELP! Brownian motion. Molecular motion is invisible in itself. When a small particle is suspended in a fluid, bombardment by molecules makes the particle jitter about at random. Robert Brown discovered this motion in 1827 while studying plant...

I am quite well versed with the random walk problem and am interested in finding out more about Brownian motion. Does anyone have any suggestions for books that explain Brownian motion in detail? I suspect these will be books on statistical mechanics.

If Brownian motion is continuous, why then is it not inherently deterministic? Are the events that Brownian motion covers based on previous states and causal factors? So, unpredictable (too many variable at play), yet causal? What am I missing here?

Homework Statement Let Bt be a standard Brownian motion. Let s<t: a) Compute P(\sigma B_{t}+\mu t|B_{s}=c) b) Compute E(B_{t}-t|B_{s}=c) Homework Equations Defition of brownian motion: B(t) is a (one-dim) brownian motion with variance \sigma^{2}if it satisfies the following conditions: (a)...

Hi, I'm trying to prove that X=(X_{t})_{t\geq0} is a Brownian Motion, where X_{t} = tB_{1/t} for t\neq0 and X_{0} = 0. I don't want to use the fact that it's a Gaussian process. So far I am stuck in proving: \[ X_{t}-X_{s}=X_{t-s} \quad \forall \quad 0\leq s<t \] Anyone has any ideas?

Homework Statement Show that \frac{X ( a^2t) }{a} is a brownian motion.Homework Equations http://img168.imageshack.us/img168/8453/83818601fz4.png The Attempt at a Solution I found this in my lecture notes but isn't the proof just replacing (t-s) by a^2(t-s) and s by a^2 s and dividing...

The brownian motion setup using smoke and air particles represents and allow us to conclude that gaseous particles move randomly (in any direction). Is there a setup using other particles and another fluid instead of smoke and air to represent the movement of liquid particles? 1) Can we...

Hi all. My teacher briefly mentioned brownian motion a few days ago but didn't really go in depth. I am planning to do my final paper on this topic and I just have a few questions. Hopefully, someone can point me in the right direction. 1. Let's suppose I have a container of water and some...

I'm reading an old, maybe outdated, paper by Karl Popper about the 2. law of thermodynamics, brownian motion and perpetual motion. Popper writes: Before that, Popper has described Planck's law as: So, my question is: Is brownian motion considered to be a violation to the 2. law of...

http://arxiv.org/abs/0710.1904 Relativistic generalization of Brownian Motion Authors: T. Koide, T. Kodama 11 pages (Submitted on 10 Oct 2007) "The relativistic generalization of the Brownian motion is discussed. We show that the transformation property of the noise term is determined by...

HI, i would need some help to solve the Brownian motion given by the Weiner Integral(over paths): \int \mathcal D [x_{t}]exp(-\int dt (m/2(\dot x)^{2}-V(x)) for the case V(x)=\delta (x) +\delta (x-1)+\delta (x-2) any help would be appreciated, thanks

Hi all, I need help with a question. Let B(t), t>= 0 be a standard Brownian motion and let u, v, w > 0. Calculate E[B(u) B(u+v) B(u+v+w)], using the fact that for a zero mean normal random variable Z, E[Z^3] = 0. I tried to do this question by breaking up the brownian motions, i.e...

In one of my homework problems it is a problem under the section of Brownian motion. It asks me to compute the average velocity of particles! here is the exact problem: The average speed of hydrogen molecules at 0 degrees C' is 1694 m/s. Compute the average speed of colloidal particles of...

I have read the next article and i want to realice the same calculation but i have some doubt www.chemengr.ucsb.edu/people/faculty/squires/public_html/laugasquires05.pdf In the section II. Image systems near a partial slip surface subsection a. Set up and boundary conditions A doubt it's...

hey there, i'm curious as to why they call it fractional Brownian motion. please don't say its Brownian motion that is fractional :-p many thanks

I know that this site is not for speculation, but can someone help me in this doubt ?:rolleyes: I know that perpetual motion of secod kind is considerated impossible. So I would like to know why what are descripted under doesn't work. I've a small permanent magnet that can remain in...

Describe the process of simulating a brownian motion with drift of 4 units and diffusion of 2 units. write a program in any application to imulate such a brownian motion. Anyone knows where should i start first if i use excel to do it. I don't know what equation to use.

Let's say we restrict 6 coin tosses to a period t so that each toss will take \frac{t}{6} . The size of the bet is \sqrt{\frac{t}{6}} Then why does \sum^n_{j=1} (S_{j}-S_{j-1})^{2} = 6 \times(\sqrt{\frac{t}{6}}) = t . Or more generally why does: \sum^n_{j=1}(S_{j}-S_{j-1})^{2} =...

A while back, I pointed out a paper in the Relativity section of PF that claimed to have a description of Special Relativity that is meant for "school-going children". It seems that such activity is a popular one for researchers at the Tata Institute of Fundamental Research in Mumbai, India...