A 1D diffusion process of the form

$$dX_t = -V'(X_t)dt + \sigma dW_t$$

can be used to describe the movement of a particle in potential $V(x)$. The stationary density is then $$\pi(x) = Me^{V(x)/\sigma^2}$$ where $M$ is a normalizing constant [1, p. 57]

To what extent and under which assumptions can this be generalized to multivariate diffusion processes?

I have some bivariate data that I assume is generated by a potential of no particular functional form. So, basically I have an approximate stationary density, and I would like to get a non-parametric estimate for the underlying potential landscape.

Source: [1] Iacus (2008) Simulation and inference of stocastic differential equations


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.