Related papers: Coupling, local times, immersions
By developing a new technique called the bi-coupling argument, we estimate the relative entropy between different diffusion processes in terms of the distances of initial distributions and drift-diffusion coefficients. As an application,…
In this paper, we study some control problems that derive from time optimal control of coupled spin dynamics in NMR spectroscopy and quantum information and computation. Time optimal control helps to minimize relaxation losses. The ability…
A closed-form solution to the energy-based stochastic Schrodinger equation with a time-dependent coupling is obtained. The solution is algebraic in character, and is expressed directly in terms of independent random data. The data consist…
In this paper, we utilize event-triggered coupling configuration to realize synchronization of linearly coupled dynamical systems. Here, the diffusion couplings are set up from the latest observations of the nodes of its neighborhood and…
Many systems of physical and biological interest are characterized by assemblies of phase oscillators whose interaction is mediated by a diffusing chemical. The coupling effect results from the fact that the local concentration of the…
We propose a new simple construction of a coupling at a fixed time of two sub-Riemannian Brownian motions on the Heisenberg group and on the free step 2 Carnot groups. The construction is based on a Legendre expansion of the standard…
We study the properties of a refined weak coupling limit that preserves complete positivity in order to describe non-Markovian dynamics in the spin-boson model. With this tool, we show the system presents a rich and new non-Markovian…
We discuss a few mathematical aspects of random dynamical decoupling, a key tool procedure in quantum information theory. In particular, we place it in the context of discrete stochastic processes, limit theorems and CPT semigroups on…
Excess pore pressure in granular--fluid mixtures can transiently suppress frictional contacts and dramatically enhance flow mobility, yet its evolution is commonly modeled using constant effective diffusivities. Here we show that the…
Excursion reflected Brownian motion (ERBM) is a strong Markov process defined in a finitely connected domain $D \subset \C$ that behaves like a Brownian motion away from the boundary of $D$ and picks a point according to harmonic measure…
We study a simple singular control problem for a Brownian motion with constant drift and variance reflected at the origin. Exerting control pushes the process towards the origin and generates a concave increasing state-dependent yield which…
We discuss the optimal Markovian coupling before an exponential time of the Kolmogorov diffusion, and a class of related stochastic control problems in which the aim is to hit the origin before an exponential time. We provide a scaling…
Spatial patterning and synchronization are pervasive features of plankton communities, yet the mechanisms that allow such patterns to persist coherently under environmental noise remain unresolved. In vertically structured aquatic…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
The oscillatory dynamics of natural and man-made systems can be disrupted by their time-varying interactions, leading to oscillation quenching phenomena in which the oscillations are suppressed. We introduce a framework for analyzing,…
Prompted by an example arising in critical percolation, we study some reflected Brownian motions in symmetric planar domains and show that they are intertwined with one-dimensional diffusions. In the case of a wedge, the reflected Brownian…
The two-dimensional Brownian loop-soup is a Poissonian random collection of loops in a planar domain with an intensity parameter c. When c is not greater than 1, we show that the outer boundaries of the loop clusters are disjoint simple…
We consider the simulation of distributions that are a mixture of discrete and continuous components. We extend a Metropolis-Hastings-based perfect sampling algorithm of Corcoran and Tweedie to allow for a broader class of transition…
We present a semi-analytical framework for computing the coupling of radiative and guided waves in slowly varying (nearly uniform or nearly periodic) surfaces, which is especially relevant to the exploitation of nonlocal effects in…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…