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1 vote
1 answer
387 views

SDE with non-degenerate diffusion visits every point

I am asking an extension of the question here for SDEs of the Ito form. Consider the SDE $dX_t =\sigma(X_t) dW_t$, where $W$ is a $d$-dimensional Brownian motion and $\sigma:\mathbb{R}^n\to \mathbb{R}...
John's user avatar
  • 503
2 votes
3 answers
470 views

Existence of solution to SDE with perscribed initial and terminal conditions

The SDEs \begin{equation} dZ_t = \mu(t,Z_t)dt + \sigma(t,Z_t)dW_t \end{equation} with prescribed initial conditions are well studied. My question came up in my research and I have not found much on ...
ABIM's user avatar
  • 5,405
1 vote
1 answer
482 views

Wong-Zakai smooth approximation in probabilty for stochastic differential equations

I'm looking for a result of the form: Let $B_\epsilon$ denote a "natural" smooth $\epsilon$-approximation to an $n$-dimensional Brownian motion $B$ (e.g. by mollification or simply piecewise linear) ...
Tyr Curtis's user avatar