Guiding techniques for conditioning Markov processes
Conditioning Markov processes is an important aspect in the statistical analysis of processes that develop continuously in time. Mathematician Marc Corstanje and his colleagues have done research into conditioning processes to be at a fixed time at a fixed location.
The research is a combination of formulating technical proofs of theorems that were in many cases complemented by numerical simulations.
Conditions were given that are sufficient for simulating processes conditioned on a state in the future. This was then applied in various situations such as chemical reaction processes and processes that develop in curved spaces. In addition, various applications were demonstrated for the statistical analysis of such processes.
The study is part of a larger research into the control of stochastic processes. The conditions that were formulated are the most general ones so far in the context of finite dimensional Markov processes. Further applications in the field of statistics for stochastic processes can be built upon.
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