Abstract:Inferring a diffusion equation from discretely observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments.
Assuming that the underlying dynamical process obeys a d-dimensional stochastic differential equation of the form dx_t = b(x_t)dt + \Sigma(x_t)dw_t, we propose neural network-based estimators of both the drift b and the spatially-inhomogeneous diffusion tensor D = \Sigma\Sigma^T/2… Show more
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