Stochastic Definition and 143 Threads

Hello all, I have run into this problem, and being that I know nothing about stochastic DiffyQ I am trying to toy around with it. Basically, the following is a boiled down version of my problem: I have a probability density function that is given: p(t) and let's say we pick 1 value from...

Hi, there. I am not major in physics so maybe I lack some basic knowledge. Imagine one have an ideal sensor, which can convert the emission to some kinds of signal (typically, voltage), then what process can describe the measure data? Is it related to...

1. Assume that earthquakes strike a certain region at random times that are exponentially distributed with mean 1 year. Volcanic eruptions take place at random times that are exponentially distributed with mean 2 years. What is the probability that there will be two earthquakes before the next...

Homework Statement 1. Assume that earthquakes strike a certain region at random times that are exponentially distributed with mean 1 year. Volcanic eruptions take place at random times that are exponentially distributed with mean 2 years. What is the probability that there will be two...

I am learning Stochastic Processes right now. Can someone some explain why waiting time is memoryless? Say, if a light bulb has been on for 10 hours, the probability that it will be on for another 5 is the same as the 1st 5 hours. It doesn't make sense to me, because the longer you use it...

Homework Statement Calculate the Kalman-Bucy Filter equations Homework Equations F=(0 1)' K is unknown but y = X_1 + d/dt(v) E=((Fw-Kv)(Fw-Kv)')=FQF' + KRK' Q = E(ww') and R = E(vv') The Attempt at a Solution There is more to this question but I am just having trouble understanding where Q...

Hi, I have several sets of stochastic signals that oscillate about the x-axis over time. I would like to transform these signals into the frequency domain (make a periodogram) so that I can which signal has the most stable frequency. I was thinking about using taking the Fourier transform...

This semester I have a course on mathematical methods in physics. It's in three parts and the first professor is talking about Markov processes (discrete and continuous time) and diffusion. The problem is he doesn't have any notes or a reference textbook. Do you know any textbook on these topics?

Hi to everybody, I'm going to apply for the theme mentioned in the title during my study and further by writing scientific works. Also I'm very excited with it because of its applications. Couldn't anyone suggest some literature for beginners in Stochastic Calculus? P.S. I also have some...

If we have a DE of the following form: \frac{dX}{dt}=b(t,X_t)+\sigma(t,X_t).W_t and look for a stochastic process to represent the (second) noise term. Now my textbook tells me that the only process with 'continuous paths' is Brownian motion. The noise term denotes random, indeterministic...

hello if we have set of stochastic variables representing the random time it takes to do something: X,Y,Z,W and C where C is the sum of X Y Z W, thus the time it takes to do these things in sequence. If: X: N(30,5) Y: N(30,3) Z: N(20,2) W: N(40,7) makes C adding these together right, mean plus...

Homework Statement How to solve this SDE? dX_t = [1/X_t] dt + aX_t dB_t Homework Equations The Attempt at a Solution If I didnt get it wrong, this is not a general linear SDE, and my course in elementary stochastic calcus did not cover SDEs other than the general linear ones...

Homework Statement Suppose that passengers arrive at a train terminal according to a poisson process with rate "$". The train dispatches at a time t. Find the expected sum of the waiting times of all those that enter the train. Homework Equations F[X(t+s)-X(s)=n]=((($t)^n)/n!)e^(-$t))...

In the attached equations, for the second last step to the last step why dSdS=sigma2S2dt ?

The attachment is from Shreve's stochastic calculus book In the attachment what does the symbol ^ mean? Thanks

Dear Community, I am faced with a challenge. I can't quite grasp the implications of this. I schould've listened better in statistics lectures! :blushing: I would really appreciate your help. :) I have a not normal stochastic process P on which I can bet. Obviously, I don't know the...

Can we consider a stochastic process being chaotic? consider evolution of only two particular systems with closed initial states (not ensemble or statistical properties of the system)

Can someone explain to me the rigorous meaning of statements like: dt^2 = 0 dW*dt = 0 dW^2 = dt Here W = W(t) is standard Brownian motion. I know that a SDE such as dX = f dW + g dt rigorously means X(t) = X(0) + \int_0^tfdW + \int_0^tgds But what does dt^2 mean? And why...

Would anyone have any resources on the stochastic interpretation of quantum mechanics? It appears to be a relatively new interpretation, proposed this year by Roumen Teskov, based on John Wheeler's "quantum foam." That's really the extent of the information I have, and I'm curious to find...

From my extremely small and inadequate knowledge of stochastic processes (and Wikipedia): A stochastic process is a process in which some later state is determined by predictable actions and by a random element. Now the question: this "random element" is this meant to compensate for...

Hi, A quick question regarding random functions. Suppose \xi(t) is a stochastic function. In other words, its value at time t is random with some known distribution (Gaussian, say). Is there any way of calculating \frac{d\xi}{dt}? Thanks,

I would like to construct a model using a markov chain that has different stochastic processes for each state in the chain. Is there a term for such a thing, or anything similar to it? Thanks

I had this problem on my last midterm and received no credit for these parts. 1. Express trains arrive at Hiawatha station according to a Poisson process at rate 4 per hour, and independent of this, Downtown local buses arrive according to a Poisson process at rate 8 per hour. a. Given that 10...

Hi there, I'm starting revision for Stochastic Analysis and have a few questions relating to the notes I'm reading. I'd much appreciate any clarification as I'm not as up to speed as I'd like. 1) In the definition of classical Wiener space I have H=L_{0}^{2,1}([0,T]; \mathbb{R}^{n}) the...

Suppose that A and B follow geometric brownian motion, where zA, and zB follow wiener process dA/A=a*dt+b*dzA dB/B=c*dt+d*dzB dzA*dzB=e*dt What stochastic process does A/B follow? This is not a homework question(I am sure it's almost trivially easy to those who learned the stuff). I am very...

Homework Statement Question: 18. Show that every 2 x 2 stochastic matrix has at least one steady-state vector. Any such matrix can be written as P = |1-a b | | a 1-b | where a and b are constants between 0 and 1. (There are two linearly independent steady-state...

Homework Statement http://img411.imageshack.us/img411/4274/50122514bc3.png Homework Equations http://img133.imageshack.us/img133/4624/68596500xm4.png The Attempt at a Solution I don't know how to start I've found this: Let X be the the winnings per bet and let the total profit...

Homework Statement I know that per definition E(N)= \sum P(N=k) \cdot k . But how can I rewrite the above expectation towards the 'usual definition'?

I am taking a project this year. As the title suggests this project is a maths project but I was wondering if anyone can direct me to some science field in which I could use stochastic models. I have very limited knowladge in science so something theoretical would be nice. Any books would be...

Homework Statement This is a question about one single step of a solution of a long equation. http://www.geocities.com/link_herooftime/math.jpg where P, U and V are variables. a, b, c, d are constants and t is the time, which are measured in discrete periods. The question is how...

Hi, I have a random grid, meaning that each cell consists of a random number. I need to evaluate the gradient. I've tried to apply a basic Euler formula (u_(i+1) - u_(i-1))/2dx but since the values can fluctuate a lot, fluctuations are even stronger for the gradient... I'm thinking...

Hi all, Im going to be researching into Stochastic processes don't know anything about it except the title, Thought I might get on here to get an introduction, see what other people know about it and tips that would be helpful in understanding the concepts? so if anybody knows anything about...

I was reading through the section of my linear algebra book that deals with Markov chains. It said that in a stochastic matrix A, there is always a probability vector v such that Av = v. I didn't see a precise definition of a stochastic matrix, but I gather it means that every entry is...

hi, i took calc 3 and differential equations. that was about a year ago and i vaguely remember what that's about. I'm thinking about electrical engineering and i heard from many that its math intensive. can someone tell me exactly what math is involved? i've been told to look into classes...

What is the path of study to understand stochastic calculus? I bought the book "Elementary Stochastic Calculus with Finance in View" (Mikosch) because it was touted as a non rigorous introduction to stochastic calculus, and I spent three days trying to decipher the first two pages. :(

Hello I would love to know the basics of how to solve stochastic differential equations. Also what importance does the Ito integral lend to this matter? Thanks for any help!

Hello all I am doing a project concerning volatility and drift structure of various markets. If we have dr = u(r,t)dt + w(r,t)dX is this a partial differntial equation or just a differential equation? r is the spot rate t is time and X is a random variable. Thanks :smile:

Hello all Let's say we define a stochastic integral as: W(t) = \int^{t}_{0} f(\varsigma)dX(\varsigma) = \lim_{n\rightarrow\infty} \sum^{n}_{j=1} f(t_{j-1})(X(t{j})) - X(t_{j-1})) with t_{j} = \frac{jt}{n} IS this basically the same definition as a regular integral? Also if we have...

Hello all If you throw a head I give you $1. If you throw a tail you give me $1. If R_i is the random amount ($1 or -$1) you make on the ith toss then why is: E[R_i] = 0, E[R^2_i]=1, E[R_iR_j] = 0 ? If S_i = \sum^i_{j=1} R_j which represents the total amount of money you have won up to...

I've been trying to solve this problem for a week now, but haven't been able to. Basically I need to prove that a certain process satisfies Chapman-Kolmogorov equations, yet it isn't a Markov Process (it doesn't satisfy the Markovian Property). I attached the problem as a .doc below...

Whether somebody knows what equally <int(F*Fcomp)dx>. Where F(x,t) is complex function: F=F1+i*F2, Fcomp=F1-i*F2. F satisfies to the next linereal stochastic partial differential equation: i*h*Ft=-a*(Fxx-2*n*Fx/x+(n+1)*F/x/x)+U*F int - sing of integral by dx, Ft - first...

Prompt please where it is possible to find algorithm of the numerical decision of stochastic Shrodinger equation with casual potential having zero average and delta – correlated in space and time? The equation: i*a*dF/dt b*nabla*F-U*F=0 where i - imaginary unit, d/dt - partial...

Dear frends! Prompt please references to works in which it was considered the Schrodinger equation with stochastic (random) Gaussian delta-correlated potential which time-dependent and spaces-dependent and with zero average (gaussian delta-correlated noise). I am interesting what average wave...