4 papers
Smoothness and other hyperparameter estimation for inverse problems related to data assimilation
Baptiste Simandoux, Nikolas Kantas, Dan Crisan
We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent…
Particle Filtering for a Class of State-Space Models with Low and Degenerate Observational Noise
Abylay Zhumekenov, Alexandros Beskos, Dan Crisan +2
We consider the discrete-time filtering problem in scenarios where the observation noise is low or degenerate. We focus on the case where the observation equation is a linear funct…
Uniqueness of the solution of the filtering equations in spaces of measures
Dan Crisan, Etienne Pardoux
Nonlinear filtering is a pivotal problem that has attracted significant attention from mathematicians, statisticians, engineers, and various other scientific disciplines. The solut…
The identification of diffusions from imperfect observations
Dan Crisan, Martin Clark
This paper studies the identification of an -valued diffusion when a running function of it, say , is observed. A point-wise observation of the process (i…