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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 ...
Marco's user avatar
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2 votes
1 answer
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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 $...
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1 vote
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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 ...
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1 vote
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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 ...
Anton's user avatar
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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\})=\...
Andrea Aveni's user avatar