In geographical epidemiology, disease counts are typically available in discrete spatial units and at discrete time-points. For example, surveillance data on infectious diseases usually consists of weekly counts of new infections in pre-defined geographical areas. Similarly, but on a different...

We study the continuous-time limit of a class of Markov chains coming from the evolution of classical open systems undergoing repeated interactions. This repeated interaction model has been initially developed for dissipative quantum systems in Attal and Pautrat (2006) and was recently set up...

A systematic Bayesian framework is developed for physics constrained parameter inference of stochastic differential equations (SDE) from partial observations. Physical constraints are derived for stochastic climate models but are applicable for many fluid systems. A condition is derived for...

We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally unknown. We propose an importance sampling approach with an...

We describe a method of approximation of strong solutions to Stratonovich differential equations, that depends only on the Brownian motion defining the equation. h being the step size, it is known that the order of convergence of such approximations is h in the general case, and of h in some...

We propose a method for the simultaneous estimation of the drift and diffusion coefficients of stochastic differential equations (SDE) from panel data. The method involves matching the distribution of the experimental/field data with a panel of simulated data generated by a Monte Carlo...

We consider the problem of how to prize general securities whose payoff at maturity only depends on the interest rate rT at the time of exercise, where rt is supposed to be a stochastic Feller process. We show how to generalize the results of Cox et al. [Econometrica 53 (2) (1985) 385] regarding...

We obtain upper and lower bounds for the density of a functional of a diffusion whose drift is bounded and measurable. The argument consists of using Girsanov’s theorem together with an Itô–Taylor expansion of the change of measure. One then applies Malliavin calculus techniques in a...

Maximum likelihood estimation of discretely observed diffusion processes is mostly hampered by the lack of a closed form solution of the transient density. It has recently been argued that a most generic remedy to this problem is the numerical solution of the pertinent Fokker–Planck (FP) or...