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...
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...