Related papers: Stochastic monotonicity from an Eulerian viewpoint
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…
In this paper, we study the stochastic Hamiltonian flow in Wasserstein manifold, the probability density space equipped with $L^2$-Wasserstein metric tensor, via the Wong--Zakai approximation. We begin our investigation by showing that the…
We experimentally study the fluctuations of the work done by an external Gaussian random force on two different stochastic systems coupled to a thermal bath: a colloidal particle in an optical trap and an atomic force microscopy cantilever.…
On the basis of a dilatation invariant Lagrangian, governed equations are determined for probability density and gauge potential of the non-stationary self-similar stochastic system. It is shown that an automodel regime is observed at small…
Turbulence has associated chaotic features. In the past couple of decades there has been growing interest in the study of these features as an alternative means of understanding turbulent systems. Our own input to this effort has been in…
We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or $B_{r}$-contracting drift terms. While classical results often assume constant diffusion…
A system (P_a: a in A) of probability measures on a common state space S indexed by another index set A can be ``realized'' by a system (X_a: a in A) of S-valued random variables on some probability space in such a way that each X_a is…
Stochastic ordering among distributions has been considered in a variety of scenarios. Economic studies often involve research about the ordering of investment strategies or social welfare. However, as noted in the literature, stochastic…
A new concept of {\em an evolution system of measures for stochastic flows} is considered. It corresponds to the notion of an invariant measure for random dynamical systems (or cocycles). The existence of evolution systems of measures for…
The logistic map is a nonlinear difference equation well studied in the literature, used to model self-limiting growth in certain populations. It is known that, under certain regularity conditions, the stochastic logistic map, where the…
A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion…
Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger…
We study dynamic measure transport for generative modeling: specifically, flows induced by stochastic processes that bridge a specified source and target distribution. The conditional expectation of the process' velocity defines an ODE…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
First order stochastic dominance and monotone likelihood ratio are two partial orders on the $n$-probability simplex that play an important role in the establishment of structural results for MDPs and POMDPs. We study the strength of those…
This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…
It is shown that the inert properties of a stationary random process can be expressed in terms of the ratio of its correlation interval to the doubled variance. When using a fixed value of the Planck constant h as a proportionality factor,…
In studying randomized search heuristics, a frequent quantity of interest is the first time a (real-valued) stochastic process obtains (or passes) a certain value. The processes under investigation commonly show a bias towards this goal,…
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…
A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation…