A Path-Integral Approach to the Cameron-Martin-Maruyama-Girsanov Formula Associated to a Bilaplacian

We define the Wiener product on a bosonic Connes space associated to a Bilaplacian and we introduce formal Wiener chaos on the path space. We consider the vacuum distribution on the bosonic Connes space and show that it is related to the heat semigroup associated to the Bilaplacian. We deduce a Cameron-Martin quasi-invariance formula for the heat semigroup associated to the Bilaplacian by using some convenient coherent vector. This paper enters under the Hida-Streit approach of path integral.

A Girsanov transformation for birth and death on a Brownian flow

We consider a system of particles in birth and death on a Brownian flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of counting measures. The system depends on a handful of parameters including a rate of drift, diffusion, birth, and killing. We exhibit a Girsanov formula for the absolutely continuous change of particle system by way of a change of drift, birth, and killing rates. We can only allow for a restrictive change of drift on the flow, but for fairly unrestrictive change of birth and death rates. The result is therefore of some interest in problems of statistical inference from passive transport of transient tracers.

A Girsanov transformation for birth and death on a Brownian flow

We consider a system of particles in birth and death on a Brownian flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of counting measures. The system depends on a handful of parameters including a rate of drift, diffusion, birth, and killing. We exhibit a Girsanov formula for the absolutely continuous change of particle system by way of a change of drift, birth, and killing rates. We can only allow for a restrictive change of drift on the flow, but for fairly unrestrictive change of birth and death rates. The result is therefore of some interest in problems of statistical inference from passive transport of transient tracers.

Change of measure up to a random time: theory

Change of measure up to fixed times or stopping times is the theme of the famous Cameron–Martin–Girsanov formula. The paper studies change of measure up to random times which are not stopping times of the natural filtration. The ultimate aim is to build up a family of interesting models for physics and chemistry.