All Questions
5 questions with no upvoted or accepted answers
2
votes
0
answers
192
views
Multiple Wiener integral as Witt polynomial of Brownian motion
I know that if i have a Brownian motion $W_t$ the multiple Wiener integral
$\int_0^t \int_0^{\xi_1}...\int_0^{\xi_n} dW_{\xi_1}...dW_{\xi_n}$
can be expressed as $H_n(\int_0^t dW_s)$ where $H_n$ is ...
2
votes
1
answer
803
views
On Riemann integration of stochastic processes of order $p$
Let $x:[a,b]\times\Omega\rightarrow\mathbb{R}$ be a stochastic process, where $\Omega$ is the sample space from an underlying probability space. Let $L^p$ be the Lebesgue space of random variables on $...
1
vote
0
answers
122
views
Derivative with respect to initial condition for the solution of an SDE
Suppose we have an SDE (assuming the Lipschitz continuous conditions required for the existence of the solution):
\begin{align}
dX_t = \mu(X_t,t)dt + \sigma(X_t,t)dW_t
\end{align}
and define its ...
1
vote
0
answers
251
views
Inflated independent samples for Monte Carlo estimation
In my particular problem, running an MCMC is too expensive, so I'm looking for a simple MC estimator, which would partially inherit the correlated samples of MCMC, yet would not require computing ...
0
votes
0
answers
255
views
Distribution of "occupation times" of Brownian Motion
Let $B_t(\omega)$ be a standard Brownian motion and let $A\in\mathcal{B}(\mathbb R)$ be a Borel set.
I would like to find the distribution of $$Y_A(\omega):=\lambda(\{t\in[0,1]:B_t(\omega)\in A\})=\...