Related papers: An explicit Skorokhod embedding for functionals of…
We use active microrheology to determine the frequency dependent moduli of a linear viscoelastic fluid in terms of the polymer time constant ($\lambda$), and the polymer ($\mu_p$) and solvent viscosity ($\mu_s$), respectively. We measure…
The CEV model is given by the stochastic differential equation $X_t=X_0+\int_0^t\mu X_sds+\int_0^t\sigma (X^+_s)^pdW_s$, $\frac{1}{2}\le p<1$. It features a non-Lipschitz diffusion coefficient and gets absorbed at zero with a positive…
Thermodynamic inference from coarse observations remains a key challenge. Memory, in particular correlations between consecutively observed mesostates, blur signatures of irreversibility and must be accounted for in defining physical…
A hallmark of integrable systems is the purely elastic scattering of their excitations. Such systems possess an extensive number of locally conserved charges, leading to the conservation of the number of scattered excitations, as well as…
In this manuscript, we determine the optimal approximation rate for Skorohod integrals of sufficiently regular integrands. This generalizes the optimal approximation results for It\^o integrals. However, without adaptedness and the It\^o…
We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions and we show that…
In this article, we combine the perspectives of density, entropy, and multifractal analysis to investigate the structure of ergodic measures. We prove that for each transitive topologically Anosov system $(X,f)$, each continuous function…
This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…
In this article, we introduce an infinite-dimensional analogue of the $\alpha$-stable L\'evy motion, defined as a L\'evy process $Z=\{Z(t)\}_{t \geq 0}$ with values in the space $\mathbb{D}$ of c\`adl\`ag functions on $[0,1]$, equipped with…
The embedding problem for Markov chains is a famous problem in probability theory and only partial results are available up till now. In this paper, we propose a variant of the embedding problem called the reversible embedding problem which…
Comparison results are given for time-inhomogeneous Markov processes with respect to function classes induced stochastic orderings. The main result states comparison of two processes, provided that the comparability of their infinitesimal…
The partial stochastic realization of periodic processes from finite covariance data has recently been solved by Lindquist and Picci based on convex optimization of a generalized entropy functional. The meaning and the role of this…
In this work we study orbit recovery over $SO(3)$, where the goal is to recover a function on the sphere from noisy, randomly rotated copies of it. We assume that the function is a linear combination of low-degree spherical harmonics. This…
A notion of convergence of excursion measures is introduced. It is proved that convergence of excursion measures implies convergence in law of the processes pieced together from excursions. This result is applied to obtain homogenization…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
The purpose of this paper is to develop a new effective approach to higher-order mixing in the semisimple setting. We prove effective exponential mixing of all orders for partially hyperbolic algebraic actions, under a strong spectral-gap…
We study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratchets based on fractional subdiffusion within a generalized non-Markovian Langevin equation approach. A corresponding multi-dimensional Markovian…
The study of both sensitivity analysis and differentiability of the stochastic flow of a reflected process in a convex polyhedral domain is challenging because the dynamics are discontinuous at the boundary of the domain and the boundary of…
We investigate the trajectory-level dynamics of a double quantum dot system using the newly developed formalism of stochastic excursions. This approach extends full counting statistics by enabling a filtering of complex trajectories into…
We solve explicitly the following problem: for a given probability measure mu, we specify a generalised martingale diffusion X which, stopped at an independent exponential time T, is distributed according to mu. The process X is specified…