Random walk Definition and 97 Threads

http://img844.imageshack.us/img844/8333/1111jx.png Homework Statement With which probability, starting in g, node d gets hit before node e?Homework Equations The Attempt at a Solution I think the probability of hitting each node starting in g is the following: p(g) = 1 p(c) = 1/2 p(a) =...

Hello Everyone, The following is a subproblem of research project I'm working on, i.e. not a homework. Let's suppose you have a bounded 2d plane and n distinct probes that do random-walk in that plane. The world is closed in a sense that a probe going outside the border ends up being on the...

Hi all: Now I have a question about the concept of diffusion coefficient in two cases: the diffusion equation (J=DdT/dx) and the random walk (tao^2=6Dt). My quesion is the two D in two equations are the same or different. If they are different, is there any relationship between them? Best Xu

Hi guys, I'm doing some thinking about random walk. Imagine there is a bounded 2D plane and a single spawn point. The spawn produces units which must bring in minerals scattered around the spawn. The locations of minerals are not known, so the units diffuse randomly away from the spawn...

Suppose X is a random walk with probability P(X_k=+1)=p and P(X_k=-1)=q=1-p and S_n=X_1+X_2+...+X_n Can anyone explain why does line 3 equal to line 4? P(S_k-S_0≠0 ,S_k-S_1≠0 ,…,S_k-S_{k-1}≠0) =P(X_k+X_{k-1}+⋯+X_1≠0 ,X_k+X_{k-1}+⋯+X_2≠0 ,…,X_k≠0) =P( X_k≠0 ,X_k+X_{k-1}≠0...

Hi guys, I was reading about random walks and i encountered one step of a proof which i don't know how to derive in a mathematically rigorous way. the problem is in the attached file and S is a random walk with X_i as increments, X_i = {-1,+1} I know that intuitively we can switch the...

I've been trying to find the solution to the following problem but it's evaded me thus far. Take the classic one dimension random walk scenario. I start at point 0 and can either step forward +1 step or step backwards -1 step (equal probability). I can countinue like this for N steps. If...

I'm reading a stat textbook and it says the following: Let a discrete-time random walk be defined by Xt = Xt-1 + et, where the et's are i.i.d. normal(0,σ2). Then for t≧1, (i) E(Xt) = 0 (ii) Var(Xt) = t σ2 However, the textbook doesn't have a lot of justifications for these results and...

Homework Statement Hello, I was reading Feynman's lectures on physics, and I'm having trouble following some deductions in the part about Probability. The random walk is a problem in which someone starts at x = 0 ant then takes a step forward (x = 1) or backward (x = -1) and after N steps de...

Question about "random walk" Homework Statement . .. Recall that in a random walk where each step has length l, the total distance traveled after N steps is L = N1/2lHomework Equations The Attempt at a Solution My problem is the N number of steps, not sure how i would find that. I saw in the...

Hello folks, this is my first post. I'm not quite sure that I fully understand the idea of a random walk of a photon that is generated at the core of a star. I've read this: http://www3.wooster.edu/physics/jrIS/Files/Walker_Web_article.pdf My understanding of the theory is this: A...

I have created a code to simulate a scaled random walk, but I need to now modify it to generate 1000 paths and then estimate the variance with n = 100, for t = 0.25, 0.5, 0.75 and 1. Can anyone help out with how to generate all 1000 paths? Sorry if this is painfully easy, I am a complete...

Homework Statement Let us define the following random walk: Start with a randomly chosen (with uniform probability) unit vector (with respect to the usual Euclidean norm) in \mathbb{R}^n and call it x^{(0)}. Now, x^{(t+1)} is generated from x^{(t)} in the following manner - randomly and...

Hello I am trying to find an analytic expression for the probability that a particle will have passed a position x after a time t. It is a 1D random walk, the probability distribution after time t that a particle will end at position x is given by a gaussian, but I need to know how many...

Homework Statement Consider the following random walk on the integers: \mathbb{S}=\{0, 1, 2, 3, ... , L\} Let Wn = {the state k \in\mathbb{S} you are in after the n'th transition} \mathbb{P}[W_{n+1}= k \pm 1 | W_{n} = k] = \frac{1}_{2} For \ 1\leq k\leq L-1 Otherwise...

Hi, I'm trying to read into CTRW, but I'm finding the information online a little difficult to take in. From what I've read the process differs from normal random walks in that jumps take place after some waiting time \tau, which can be from 0<\tau<\infty. Would I also be right in saying that...

Hi, I have a problem (1) where I need to compute the ratio of probabilities of hitting and stopping at a positive vertical barrier x vs hitting and stopping at a negative horizontal barrier y after starting from (0,0). I feel that by symmetry, the answer to this would be the same as...

Homework Statement A clown stands at the side of a swimming pool. In his hand is a bag containing n red balls and n blue balls. At each step he puts his hand into the bag and pulls out a random ball and throws it away. If the ball is red, he makes a step towards the pool and if it is blue...

Hi, I'm modeling receptors moving along a cell surface that interact with proteins inside of a cell. I figured it would be easier to model the receptors in spherical coordinates, however I'm unsure of how to model a random walk. In cartesian coordinates, I basically model a step as: x = x +...

Hello, I have read the probability chapter in Feynman's lectures on physics. And got fascinated by the random walk. There is a statement, that in a game where either a vertical distance of +1 or -1 can be walked each move, the expected value of the absolute distance (lets call it <D>) from...

Problem: Three friends do a 1D Random Walk with p=q starting at 0. Are they guaranteed to all meet again somewhere? So all the friends are starting at 0 at the same time and we want to know if they are guaranteed to meet again anywhere in the walk. Hint: if they do meet, which places are...

I have a problem concerning a one-dimensional random walk in potentials. Assume a one-dimensional space [0,1] and a probability distribution p(x). At every point x we have a probability p(x) to go left and 1-p(x) to go right. Assume some smooth distribution of p(x) with boundaries p(0) = 0 and...

I have the intrinsic noise PSD spec for Honeywell's QA3000 accels, and I need to find the velocity random walk due to noise to show that I'm within my allowable. The PSD is given in units of g^2/Hz vs Hz. I'm given a velocity random walk due to noise spec of 15 (micro-m/s)/rt(s) that I must be...

This is for my Statistics and Stochastic Processes class, we are learning about random walk [b]1. Let p<q where p is success (+1) and q is failure (-1). Let T=last time we hit 0 (T\geq0) Find P(T=t) Then using the answer from the above question, make up a formula for \sum(2n choose...

My impression from looking through the internet is, that it is a well-accepted opinion that stock market calculations are based on the random walk hypothesis. A friend of mine says otherwise. Could you provide some opinions or rather references to prove one view or the other?

Homework Statement T_{x} is the passage time min{n : x(n) = x} for paths starting from x(0)=0 Show: \lim_{x\rightarrow +\infty}E_{0}(e^\frac{-\alpha\\T_{x}}{x^2}) = e^\-\sqrt{2\alpha} for any \alpha ≥ 0 Homework Equations The Attempt at a Solution I came up with the...

Hi, I know that the expectation E(Sn) for a one-dimensional simple random walk is zero. But what about the variance? I read in http://en.wikipedia.org/wiki/Random_walk#One-dimensional_random_walk" that the variance should be E(Sn2) = n. Why is that? Can anyone prove it? Thank you...

Homework Statement A particle's Compton wavelength arises because of the "smearing out" effect of quantum uncertainty, which can be modeled by a random walk or by Brownian noise. I think I understand this, but what I do not get is how do you arrive at a precise frequency of oscillation from...

Homework Statement I need to determine the standard deviation from the mean position value <x> in a random walk scenario. We are given that the probability of taking a step to the right is p and the probability of taking a step to left is q. Please note that p and q need not be equal. The...

Hi guys, Would you be so kind to give me a hand with the below, please? Basically I need a formula that can help me solve the following: Let's say I have a pond with many many frogs and I have been measuring the amount they can jump. The frogs jumps seem to follow a normal distribution...

How often do you return AND CROSS the origin in a random walk? Is there a probability distribution for how many times can you expect a change in the lead of a coin tossing contest between two players (heads Vs. tails)? Which is the most likely # of changes in the lead?

A random walk can be defined by the following recurrence relation, X_{t+1} = X_t + \Delta X where \Delta X \sim \mathcal{N}(0, \sigma^2). At any time t1 \geq 0 a strategist may enter, and at any time t2 > t1 a strategist may exit. The resulting profit p is given by: p(t1,t2) = X_{t2}...

I understand the mean square end-to-end distance of a polymer of stepsize b and number of units N is given by \left\langle R^{2}\right\rangle = \sum_{i,j=1}^{N} \left\langle r_{i} r_{j}\right\rangle + \left\langle \sum_{i \neq j}^{N} r_{i} r_{j}\right\rangle And that the cross terms drop...

Hi - I am trying to find the probability of hitting one of two boundaries in a simple random walk (I describe the problem precisely below). Actually, my main concern is to find the probability distribution over time to hit either one of two boundaries. I think that this is a very standard...

A grid of 4x4 is given .__.__.__.__. | | | | | .__.__.__.__. | | | | | .__.__o__.__. | | | | | .__.__.__.__. | | | | | .__.__.__.__. A ball is located at the center of the grid which is to perform a 5 step random walk with equal probability in any...

Homework Statement Say a drunk starts making his steps of equal distance from a lamppost. Assuming that each of the steps are of equal distance, and N as the total number of steps, what is the probability of him/her ending at the lamppost? Find the probability when N is even and also for...

Starting out at zero on a number line and moving in succession one unit right or left at random, what is the probability that you will eventually return to zero?

Homework Statement http://img171.imageshack.us/img171/4711/52047019pc2.png Homework Statement Homework Equations Random walk equations: Xi is i.i.d. and S_n = X_1+...+X_n and S0=0 The Attempt at a Solution I don't have a idea where to begin. I couldn't start because I don't...

Homework Statement Let (X1, X2, ..., Xn,...) be iid increments (with mean µ and variance ∂^2) of a random walk Sn=X1+X2+...+Xn. What are the expected value, variance of Sn? Prove that lim n-> ∞ Sn =+ ∞ if µ>0 and lim n-> ∞ Sn =- ∞ if µ<0 Homework Equations The Attempt at a...

Homework Statement Two drunks start out together at the origin, each having equal probability of making a step to the left or right along the x-axis. Find the probability that they meet again after N steps. It is understood that the men make their steps simultaneously. Homework Equations...

For the random walk approach to gases, liquids, or solids, why isn't there a gradient? The atoms don't jump by themselves, right? They should have to feel forces to jump...

The question: "Two men start out together at the origin, each having a 1/2 chance of making a step to the left or right along the x-axis. Find the probability that they meet again after N steps." It then says it may help to consider their relative position but I don't see how that would...

The question: "Two men start out together at the origin, each having a 1/2 chance of making a step to the left or right along the x-axis. Find the probability that they meet again after N steps." It then says it may help to consider their relative position but I don't see how that would...

I was unaware that one could obtain the Dirac equation as a result of a random walk. I believe that this has been done by other researchers, but I found it by Ord's papers: http://arxiv.org/find/quant-ph/1/au:+Ord_G/0/1/0/all/0/1 Anyone else find these interesting? My interest is due to...

Can the Hubble expansion be explained in terms of spacetime events undergoing a random walk?

Ok I have a varaition of the random problem as follows. We have a container with volume V and N particles. We consider a subvolume v and n particles. The probability of particles being inside v is (v/V) Ok I found the mean of n (mean number of molecules in v) < n > = N*v*(1/V) Then they...

We know that the standard deviation [sig] for a random walk, represented by a net distance d, to be approximately the square root of the total number of steps N, each of length L, from the origin. I. e., d~N1/2L~[sig]L. Does the angle attained after these steps also have a significant...