相关论文: Global Existence of Bell's Time-Inhomogeneous Jump…

The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are…

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via…

We prove that, contrary to the standard quantum theory of continuous observation, in the formalism of Event Enhanced Quantum Theory the stochastic process generating individual sample histories of pairs (observed quantum system, observing…

Quantum trajectory theories have not fully reconciled discrete quantum jumps with continuous unitary evolution. We address this challenge by developing a hidden variable formulation that reveals hidden correlations in individual trials. We…

The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…

Analyzing the spreading of information in many-body systems is crucial to understanding their quantum dynamics. At the most fundamental level, this task is accomplished by Bell inequalities, whose violation by quantum mechanics implies that…

We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…

In this paper we present a new model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use an Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid particles,…

This article establishes a first-principles statistical field theory of fully developed isotropic turbulence. Applying an exact Helmholtz decomposition to the local angular momentum field ($\Lvec = \rvec \times \uvec$) reveals a segregation…

We look at the equilibrium of a Brownian particle in an inhomogeneous space following the alternative approach proposed in ref.[1]. We consider a coordinate dependent damping that makes the stochastic dynamics the one with multiplicative…

In his 1972 paper, John Lamperti characterized all positive self-similar Markov processes as time-changes of exponentials of Levy processes. In the past decade the problem of classifying all non-negative self-similar Markov processes that…

Modeling the non-equilibrium dissipative dynamics of strongly interacting quantized degrees of freedom is a fundamental problem in several branches of physics and chemistry. We implement a quantum state trajectory scheme for solving…

In classical theory, the trajectory of a particle is entirely predetermined by the complete set of initial conditions via dynamical laws. Based on this, we formulate a no-go theorem for the dynamics of classical particles, i.e., a Bell's…

A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-Markovian noise, which possesses an arbitrary non-exponential distribution of the residence times, is developed. The formally exact expression…

This paper critically discusses an objection proposed by H. Nikolic against the naturalness of the stochastic dynamics implemented by the Bell-type Quantum Field Theory, an extension of Bohmian Mechanics able to describe the phenomena of…

We consider a stochastic functional delay differential equation, namely an equation whose evolution depends on its past history as well as on its present state, driven by a pure diffusive component plus a pure jump Poisson compensated…

In this paper we study a family of nonlinear (conditional) expectations that can be understood as a semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a time and path-dependent…

In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate,…

We utilize the novel non-Markovian quantum jump (NMQJ) approach to stochastically simulate exciton dynamics derived from a time-convolutionless master equation. For relevant parameters and time scales, the time-dependent, oscillatory…

Determining the Markovianity and non-Markovianity of a quantum process is a critical problem in the theory of open quantum systems, as their behaviors differ significantly in terms of complexity. It is well recognized that a quantum process…