Stochastic Definition and 166 Threads

Homework Statement I need someone to reassure me (or correct me) on this problem: The process X(t) = e^{At} is a family of exponentials depending on the random variable A. Express the mean \eta(t) , the autocorrelation R(t_1,t_2) , and the first order density f(x,t) of X(t) in terms of...

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...

Homework Statement Hi I have been working on understanding concept fra Measure Theory known as support or supp I know that according to the definition if (\mathcal{X},\mathcal{T}) is a topological space and (\mathcal{X},\mathcal{T}, \mu) such that the sigma Algebra A contain all...

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 I'm a french student, I'm actually not sure this is the good place to ask my question but as it deals with the nuclear fission I try here... don't hesitate to tell me if there is a better forum... thx.. well, I'm trying to solve numerically the Langevin equation, initially for...

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...