Related papers: On Time Reversal of Piecewise Deterministic Markov…
Symmetries have a crucial role in today's physics. In this thesis, we are mostly concerned with time reversal invariance (T-symmetry). A physical system is time reversal invariant if its underlying laws are not sensitive to the direction of…
The aim of this work is the mathematical analysis of the physical time-reversal operator and its definition as a geometrical structure\QTR{bf}{, }in such a way that it could be generalized to the purely mathematical realm. Rigorously, only…
The magnetization reversal time of ferromagnetic nanoparticles is investigated in the very low damping regime. The energy-controlled diffusion equation rooted in a generalization of the Kramers escape rate theory for point Brownian…
For Markov jump processes on irreducible networks with finite number of sites, we derive a general and explicit expression of the squared coefficient of variation for the net number of transitions from one site to a connected site in a…
In this paper we study a particular class of Piecewise deterministic Markov processes (PDMP's) which are semi-stochastic catastrophe versions of deterministic population growth models. In between successive jumps the process follows a flow…
We give a necessary and sufficient condition for a homogeneous Markov process taking values in $\R^n$ to enjoy the time-inversion property of degree $\alpha$. The condition sets the shape for the semigroup densities of the process and…
Time irreversibility, which characterizes nonequilibrium processes, can be measured based on the probabilistic differences between symmetric vectors. To simplify the quantification of time irreversibility, symmetric permutations instead of…
We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…
We study dynamical reversibility in stationary stochastic processes from an information theoretic perspective. Extending earlier work on the reversibility of Markov chains, we focus on finitary processes with arbitrarily long conditional…
The "backward simulation" of a stochastic process is defined as the stochastic dynamics that trace a time-reversed path from the target region to the initial configuration. If the probabilities calculated by the original simulation are…
We consider two approaches to study non-reversible Markov processes, namely the Hypocoercivity Theory (HT) and GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling); the basic idea behind both of them is to split…
We study a class of systems whose parameters are driven by a Markov chain in reverse time. A recursive characterization for the second moment matrix, a spectral radius test for mean square stability and the formulas for optimal control are…
The applicability of time-reversal symmetry to nonlinear optics is discussed, both from macroscopic (Maxwell equations) and microscopic (quantum theoretical) point of view. We find that only spatial operations can be applied for the…
In this paper we will describe a parallel between phenomenological and symmetry-based descriptions of the process dependence of the time-reversal-odd phenomena in QCD, such as the Sivers effect, with the goal of defining the essential…
A broken time-reversal symmetry, i.e. broken detailed balance, is central to non-equilibrium physics and is a prerequisite for life. However, it turns out to be quite challenging to unambiguously define and quantify time-reversal symmetry…
Let $X=(X_t)_{t\geq 0}$ be a known process and $T$ an unknown random time independent of $X$. Our goal is to derive the distribution of $T$ based on an iid sample of $X_T$. Belomestny and Schoenmakers (2015) propose a solution based the…
We present recent results on Piecewise Deterministic Markov Processes (PDMPs), involved in biological modeling. PDMPs, first introduced in the probabilistic literature by Davis (1984), are a very general class of Markov processes and are…
The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell biophysics. Yet, exact simulation methods, for the…
Reversal of the time direction in stochastic systems driven by white noise has been central throughout the development of stochastic realization theory, filtering and smoothing. Similar ideas were developed in connection with certain…
We study a one-dimensional Markov modulated random walk with jumps. It is assumed that amplitudes of jumps as well as a chosen velocity regime are random and depend on a time spent by the process at a previous state of the underlying Markov…