Variational formulas for the Green function

Integration formulas for the conditional transform involving the first variation

In this paper, we show that the conditional transform with respect to the Gaussian process involving the first variation can be expressed in terms of the conditional transform without the first variation. We then use this result to obtain various integration formulas involving the conditional $diamond$-product and the first variation.

Stochastic Variational Formulas for Solutions to Linear Diffusion Equations

This paper is concerned with solutions to a one dimensional linear diffusion equation and their relation to some problems in stochastic control theory. A stochastic variational formula is obtained for the logarithm of the solution to the diffusion equation, with terminal data which is the characteristic function of a set. In this case the terminal data for the control problem is singular, and h...

Function problems for Quantified Boolean Formulas

The practical use of Quantified Boolean Formulas (QBFs) often calls for more than solving the evaluation problem QBF. For this reason we investigate the corresponding function problem FQBF. We define expected outputs of FQBF instances as solution policies. We focus on the representation of policies, considering QBFs of the form ∀X ∃Y Φ. Because the explicit representation of policies for such Q...

Skolem Function Continuation for Quantified Boolean Formulas

Modern solvers for quantified Boolean formulas (QBF) not only decide the satisfiability of a formula, but also return a set of Skolem functions representing a model for a true QBF. Unfortunately, in combination with a preprocessor this ability is lost for many preprocessing techniques. A preprocessor rewrites the input formula to an equi-satisfiable formula which is often easier to solve than t...

Belief-Function Formulas for Audit Risk