arXiv subjects

Lukas Wurzer

Publications and source records attributed to Lukas Wurzer.

3 recordsLinked to original sources

arXiv2019

Random Set Solutions to Stochastic Wave Equations

This paper is devoted to three topics. First, proving a measurability theorem for multifunctions with values in non-metrizable spaces, which is required to show that solutions to stochastic wave equations with interval parameters are random sets; second, to apply the theorem to wave equations in arbitrary space dimensions; and third, to computing upper and lower probabilities of the values of the solution in the case of one space dimension.

math.PR↗

arXiv2015

Elliptic PDEs with distributional drift and backward SDEs driven by a c{à}dl{à}g martingale with random terminal time

We introduce a generalized notion of semilinear elliptic partial differential equations where the corresponding second order partial differential operator $L$ has a generalized drift. We investigate existence and uniqueness of generalized solutions of class $C^1$. The generator $L$ is associated with a Markov process $X$ which is the solution of a stochastic differential equation with distributional drift. If the semilinear PDE admits boundary conditions, its solution is naturally associated with a backward stochastic differential equation (BSDE) with random terminal time, where the forward process is $X$. Since $X$ is a weak solution of the forward SDE, the BSDE appears naturally to be driven by a martingale. In the paper we also discuss the uniqueness of a BSDE with random terminal time when the driving process is a general c{à}dl{à}g martingale.

math.PR↗

arXiv2010

Lower bound for the mean square distance between classical and quantum spin correlations

Bell's theorem prevents local Kolmogorov-simulations of the singlet state of two spin-1/2 particles. We derive a positive lower bound for the $L^{2}% $-distance between the quantum mechanical spin singlet anticorrelation function $\cos$ and any of its classical approximants $C$ formed by the stationary autocorrelation functions of mean-square-continuous, $2π$-periodic, $\pm1$-valued, stochastic processes. This bound is given by $\Vert C-\cos\Vert \geq(1-\frac{8}{π^{2}}) /\sqrt{2}\approx0.133\,95.$

quant-ph↗