相关论文: Stochastic equations generating continuous multipl…

We develop a probabilistic characterisation of trajectorial expansion rates in non-autonomous stochastic dynamical systems that can be defined over a finite time interval and used for the subsequent uncertainty quantification in Lagrangian…

Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…

We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…

We present a multiscale description of hydrodynamic turbulence in incompressible fluid based on a continuous wavelet transform (CWT) and a stochastic hydrodynamics formalism. Defining the stirring random force by the correlation function of…

We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…

A procedure to obtain the symbolic dynamics for conservative dynamical systems is introduced with reference to the standard map in a strongly chaotic regime. The method extends an approach previously developed for highly dissipative…

This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…

We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…

The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…

Turbulence is characterized by the non-linear cascades of energy and other inviscid invariants across a huge range of scales, from where they are injected to where they are dissipated. Recently, new experimental, numerical and theoretical…

"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually…

We introduce a wide family of stochastic processes that are obtained as sums of self-similar localized "waveforms" with multiplicative intensity in the spirit of the Richardson cascade picture of turbulence. We establish the convergence and…

A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…

We consider linear hyperbolic balance law that describe gas flow. Stochastic influences are introduced by series of orthogonal functions. A deterministic stabilization concept, which makes deviations at steady states decay exponentially…

This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…

We reveal that realistic fluids generate microscopic-level discontinuity constantly and the discontinuity spreads out with motion of particles rather rapidly and widely. These things cannot be treated by the standard kinetic equations, and…

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…

We provide examples of initial data which saturate the enhanced diffusion rates proved for general shear flows which are H\"{o}lder regular or Lipschitz continuous with critical points, and for regular circular flows, establishing the…

We study the convergence of stochastic time-discretization schemes for evolution equations driven by random velocity fields, including examples like stochastic gradient descent and interacting particle systems. Using a unified framework…

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…