Recent content by econmajor

Consider this Ito proces: $$dX_t = \mu(X_t,t)dt+\sigma(X_t,t)dW_t$$ with W_t being a wiener process. My question: What is the diffusion coefficient of X? My motivation for asking: A lot if financial literature refer to "diffusion coefficient" and I haven't understood by googling it, because...

Homework Statement a. Compute the limit for f(x) as b goes to 0 Homework Equations $$f(x) = \frac{(a+bx)^{1-1/b}}{b-1}$$ ##a \in R##, ##b\in R##, ##x\in R## The Attempt at a Solution ##a+bx## goes to ##a## ##1/b## goes to ##\infty## so ##1-1/b## goes to ##-\infty## ##(a+bx)^{1-1/b}## then goes...

Homework Statement $$f(x)=NormalPDF(x,2,1)+NormalPDF(x,2,(1/2)^2)$$. where NormalPDF(a,b) is the PDF for a normal distribution with mean a and variance b. Use Monte Carlo Integratoion to find: $$\int_{-10}^{10}f(x)dx$$ Homework Equations The solution to this integration is 2. I use the method...

How will a Log Euler scheme for this process look like? I still haven't a proper way to construct a simulation.

Hi Physics Forum users. I am new here and I want to use the Mathematics part of this forum. But I am not a physicist but an economist. My questions will NOT Economics related but pure mathematical and statistical. Is it OK for me to be here then and ask questions? I am active in...

Actually this is more of a simulation question but since PF doesn't have Simulation category I ask here. I need to simulate a path from a proces given by this Stochastic DE: $$ dX_t = -a(X_t-1)dt+b\sqrt{X_t}dB_t $$ where ##B_t## is wiener process/brownian motion and a and b are just some...