Recent work on path integral stochastic optimal control theory Theodorou et al. (2010a); Theodorou (2011) has shown promising results in planning and control of nonlinear systems in high dimensional state spaces. The path integral control framework relies on the transformation of the nonlinear Hamilton Jacobi Bellman (HJB) partial differential equation (PDE) into a linear PDE and the approximat...

We are grateful to the referees and Benedikt Pötscher for their helpful and constructive comments+ The research of the first author was partially supported by OTKA grants T37668 and T43037 and NSF-OTKA grant INT0223262+ The research of the second author was partially supported by NATO grant PST+EAP+CLG 980599 and NSF-OTKA grant INT-0223262+ Address correspondence to István Berkes, Graz Universi...

Integral geometry, as it is understood here, deals with measures on sets of geometric objects, and in particular with the determination of the total measure of various such sets having geometric significance. For example, given two convex bodies in Euclidean space, what is the total invariant measure of the set of all rigid motions which bring the first set into a position where it has nonempty...

We study the relative impact of small-scale random inhomogeneities and singular perturbations in nonlinear elasticity. More precisely, we analyse the asymptotic behaviour of the energy functionals Fε(ω)(u) = ∫ A ( f ( ω, x ε ,Du ) + ε|∆u| ) dx, where ω is a random parameter and ε > 0 denotes a typical length-scale associated with the variations in the elastic properties of the body. For f stati...

Preface The importance of the martingale concept cannot be overemphasized. .. . ] Martingales, Markov dependence and stationarity are the only three dependence concepts so far isolated which are suuciently general and suuciently amenable to investigation yet with a great number of deep properties. This project report deals with the stochastic calculus of semimartingales. In Doob's classical boo...

Fundamental solutions of space-time fractional diffusion equations can be interpret as probability density functions. This fact creates a strong link with stochastic processes. Recasting probability density functions in terms of subordination laws has emerged to be important to built up stochastic processes. In particular, for diffusion processes, subordination can be understood as a diffusive ...

We consider the problem of computing L1-distances between every pair of probability densities from a given family. We point out that the technique of Cauchy random projections [Ind06] in this context turns into stochastic integrals with respect to Cauchy motion. For piecewise-linear densities these integrals can be sampled from if one can sample from the stochastic integral of the function x 7→...

Stochastic differential equation (SDE) and Fokker-Planck equation (FPE) are two general approaches to describe the stochastic drift-diffusion processes. Solving SDEs relies on the Monte Carlo samplings of individual system trajectory, whereas FPEs describe the time evolution of overall distributions via path integral alike methods. The large state space and required small step size are the majo...

The aim of this work is to construct the stochastic calculus of variations on Poisson space and some of its applications via the stochastic analysis on Wiener space. We define a new gradient operator on Wiener space, whose adjoint extends the Poisson stochastic integral. This yields a new decomposition of the Ornstein-Uhlenbeck operator and a substructure of the standard Dirichlet structure on ...

We demonstrate the relevance of complex Gaussian stochastic processes to the stochastic state vector description of non-Markovian open quantum systems. These processes express the general Feynman-Vernon path integral propagator for open quantum systems as the classical ensemble average over stochastic pure state propagators in a natural way. They are the coloured generalization of complex Wiene...