Related papers: State dependent jump processes: It\^o-Stratonovich…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of…
In this paper, we study a subclass of piecewise-deterministic Markov processes with a Polish state space, involving deterministic motion punctuated by random jumps that occur at exponentially distributed time intervals. Over each of these…
We analyze the classical problem of the stochastic dynamics of a particle confined in a periodic potential, through the so called Il'in and Khasminskii model, with a novel semi-analytical approach. Our approach gives access to the transient…
Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not robust for the passage to their effective…
We study numerically stick slip motions in a model of blocks and springs being pulled slowly. The sliding friction is assumed to change dynamically with a state variable. The transition from steady sliding to stick-slip is subcritical in a…
Resetting a stochastic process is an important problem describing the evolution of physical, biological and other systems which are continually returned to their certain fixed point. We consider the motion of a subdiffusive particle with a…
We explicitly construct so-called captive jump processes. These are stochastic processes in continuous time, whose dynamics are confined by a time-inhomogeneous bounded domain. The drift and volatility of the captive processes depend on the…
Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We…
A multi-type continuous state and continuous time branching process with immigration satisfying some moment conditions is identified as a pathwise unique strong solution of certain stochastic differential equation with jumps.
We study a simple chemical reaction system and effects of the internal noise. The chemical reaction system causes the same transition phenomenon discussed by Togashi and Kaneko [Phys. Rev. Lett. 86 (2001) 2459; J. Phys. Soc. Jpn. 72 (2003)…
This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying…
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles"…
Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper [4] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of…
We study stochastic thermodynamics of a Brownian particle which is subjected to a temperature gradient and is confined by an external potential. We first formulate an over-damped Ito-Langevin theory in terms of local temperature, friction…
Stochastic systems have a control-theoretic interpretation in which noise plays the role of control. In the weak-noise limit, relevant at low temperatures or in large populations, this leads to a precise mathematical mapping: the most…
We consider a pure jump process $\{X_t\}_{t\ge 0}$ with values in a finite state space $S= \{1, \ldots, d\}$ for which the jump rates at time instant $t$ depend on the occupation measure $L_t \doteq t^{-1} \int_0^t \delta_{X_s}\,ds$. Such…
In a recent article, Krapivsky and Redner (J. Stat. Mech. 093208 (2018)) established that the distribution of the first hitting times for a diffusing particle subject to hitting an absorber is independent of the direction of the external…
The transient response of a stationary state of a quantum particle in a step potential to an instantaneous change in the step height (a simplified model for a sudden bias switch in an electronic semiconductor device) is solved exactly by…
We model continuous-time information flows generated by a number of information sources that switch on and off at random times. By modulating a multi-dimensional L\'evy random bridge over a random point field, our framework relates the…