Related papers: Stochastic analysis of surface roughness
In this article, we show how the theory of rough paths can be used to provide a notion of solution to a class of nonlinear stochastic PDEs of Burgers type that exhibit too high spatial roughness for classical analytical methods to apply. In…
In this paper we contribute a novel algorithm family, which generalizes many unsupervised techniques including unnormalized and energy models, and allows us to infer different statistical modalities (e.g. data likelihood and ratio between…
Estimating the current scene and understanding the potential maneuvers are essential capabilities of automated vehicles. Most approaches rely heavily on the correctness of maps, but neglect the possibility of outdated information. We…
Rough stochastic differential equations (rough SDEs), recently introduced by Friz, Hocquet and L\^e in arXiv:2106.10340, have emerged as a versatile tool to study "doubly" SDEs under partial conditioning (with motivation from pathwise…
We develop a new approach to characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops, i.e. loops of constant height. Given a height profile of the surface we perform independent…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
We propose a pipeline for combined multi-class object geolocation and height estimation from street level RGB imagery, which is considered as a single available input data modality. Our solution is formulated via Markov Random Field…
In this paper, we study rough path properties of stochastic integrals of It\^{o}'s type and Stratonovich's type with respect to $G$-Brownian motion. The roughness of $G$-Brownian Motion is estimated and then the pathwise Norris lemma in…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
In this paper we present nonparametric estimators for coefficients in stochastic differential equation if the data are described by independent, identically distributed random variables. The problem is formulated as a nonlinear ill-posed…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
We study the stochastic quantization of the system with first class constraints in phase space. Though the Langevin equations of the canonical variables are defined without ordinary gauge fixing procedure, gauge fixing conditions are…
Both in terrestrial and extraterrestrial environments, the precise and informative model of the ground and the surface ahead is crucial for navigation and obstacle avoidance. The ground surface is not always flat and it may be sloped, bumpy…
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density…
We investigate piecewise-linear stochastic models as with regards to the probability distribution of functionals of the stochastic processes, a question which occurs frequently in large deviation theory. The functionals that we are looking…
To aid in prediction of turbulent boundary layer flows over rough surfaces, a new model is proposed to estimate hydrodynamic roughness based solely on geometric surface information. The model is based on a fluid-mechanics motivated…
Motivated by applications in systems biology, we seek a probabilistic framework based on Markov processes to represent intracellular processes. We review the formal relationships between different stochastic models referred to in the…
The lateral position of vehicles within their lane is a decisive factor for the range of vision of vehicle sensors. This, in turn, is crucial for a vehicle's ability to perceive its environment and gain a high situational awareness by…
New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential…
Frailty models are often the model of choice for heterogeneous survival data. A frailty model contains both random effects and fixed effects, with the random effects accommodating for the correlation in the data. Different estimation…