Related papers: Stochastic monotonicity from an Eulerian viewpoint
Nontransitive choices have long been an area of curiosity within economics. However, determining whether nontransitive choices represent an individual's preference is a difficult task since choice data is inherently stochastic. This paper…
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
The characterization of intermittency in turbulence has its roots in the K62 theory, and if no proper definition is to be found in the literature, statistical properties of intermittency were studied and models were developed in attempt to…
We study stochastic choice across decision problems, each represented as a menu of action labels paired with observable outcome vectors. We propose a consistency condition for behavior in decision problems composed of two separable…
We investigate the incremental stability properties of It\^o stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two…
We develop a stochastic model for Lagrangian velocity as it is observed in experimental and numerical fully developed turbulent flows. We define it as the unique statistically stationary solution of a causal dynamics, given by a stochastic…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
A survey of the approach to Statistical Mechanics following Boltzmann's theory of ensembles and ergodic hypothesis leading to chaoticity as a unifying principle of equilibrium and nonequilibrium Statistical Mechanics.
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
Stochastic Einstein equations are considered when 3D space metric $\gamma_{ij}$ are stochastic functions. The probability density for the stochastic quantities is connected with the Perelman's entropy functional. As an example, the Friedman…
We consider the problem of tracking an unstable stochastic process $X_t$ by using causal knowledge of another stochastic process $Y_t$. We obtain necessary conditions and sufficient conditions for maintaining a finite tracking error. We…
Over the last decade, a series of applied mathematics papers have explored a type of inverse problem--called by a variety of names including "inverse sensitivity", "pushforward based inference", "consistent Bayesian inference", or…
Chaotic systems are characterised by exponential separation between close-by trajectories, which in particular leads to deterministic unpredictability over an infinite time-window. It is now believed, that such butterfly effect is not fully…
Stochastic comparisons of series and parallel systems are important in many areas of engineering, operations research and reliability analysis. These comparisons allow for the evaluation of the performance and reliability of systems under…
This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the…
This paper is concerned with the numerical approximation of stochastic mechanical systems with nonlinear holonomic constraints. Such systems are described by second order stochastic differential-algebraic equations involving an implicitly…
Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and…