An operator bound related to Feynman-Kac formulae

An Operator Bound Related to Feynman-kac Formulae

Those Fourier matrix multiplier operators which are convolutions with respect to a matrix valued measure are characterised in terms of an operator bound. As an application, the finite-dimensional distributions of the process associated with Dirac equation are shown to be unbounded on the algebra of cylinder sets. In its traditional incarnation, the Feynman-Kac formula is a means of expressing a...

A Backward Particle Interpretation of Feynman-kac Formulae

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals “on-the-fly” as well as the...

The Feynman-kac Formula in the Operator Setting

An Operator Bound Related to Regular Operators

Regular operators on L p-spaces are characterised in terms of an operator bound which is associated with certain generalisations of the Feynman-Kac formula. of multiplication by the characteristic functions of elements of the-algebra S, so that if f is a bounded S-measurable function, Q(f) = R f dQ is the operator of multiplication by f. When is it true that we can nd a positive number C such t...

Quantum Feynman-Kac perturbations