All Questions
7 questions
1
vote
0
answers
53
views
The limit ratio of two Markov Chain Probability
Suppose there are two given SDE in $\mathbb{R}^d$:
$$
\begin{align}
\left\{
\begin{aligned}
dX_t&=\begin{bmatrix}-\nabla V(X_t)+2\beta^{-1}v_F^\theta(X_t)\end{bmatrix}dt+\sqrt{2\beta^{-1}}dW_t,&...
- 303
1
vote
0
answers
766
views
Derivative of the function of random variable
Suppose we have a function $\phi(X)$ of random variable $X$. Suppose both of $\phi(X)$ and $X$ are random variables. If $\phi$ is differentiable, how to calculate the derivative of $\phi(X)$ w.r.t. $...
- 195
1
vote
1
answer
259
views
Test for OU-Process
Suppose that I'm given a sample from time-series $(x_n)_{n=1}^N$ and want to decide if it comes from an OU process or not. Is there a (rigorous) test I can use?
So far, everything I've seen is hand-...
- 5,405
0
votes
1
answer
119
views
Convergence rate estimates of Monte-Carlo first-passage time estimates
Setup
Let $X_t$ be a $d$-dimensional diffusion process solving the Ito-stochastic differential equation
$$
X_t = x+ \int_0^t f(X_t,u_t)dt + \int_0^t \sigma dW_t,
$$
where $x \in \mathbb{R}^d$, $u_t$ ...
- 5,405
2
votes
1
answer
387
views
Weak convergence of sum of log normal random variables
Let $S_t$ be the Geometric Brownian Motion, we know that
$$dS_t=rS_tdt+\sigma S_tdW_t, t\in [0,T], S_0>0, r>0,\sigma>0$$
and the distribution of $S_t$ is known explicitly. Please see the ...
- 323
4
votes
1
answer
463
views
Variance and expectation of timed-change squared Bessel process
Let $X_t$ be a squared Bessel process satisfying the SDE:
$$
dX_t=\left(1-\frac{\beta}{(1-\beta)(1-\rho^2)} \right) dt +2\sqrt{X_t}dW^{(1)}_t
$$
and $v_t=v_0e^{-\alpha^2 t/2+\alpha W^{(2)}_t}$ be a ...
- 323
0
votes
1
answer
73
views
Nonparametric estimation in diffusion
Fan and Wang
In the above paper, the Authors provide estimators for the squared spot volatility process $\left(\sigma^{2}_{t}\right)_{t\geq 0}$.
My question is how to find estimators for the process ...
