Related papers: Fourth Moment Theorem and q-Brownian Chaos
Let $X$ be a (two-sided) fractional Brownian motion of Hurst parameter $H\in (0,1)$ and let $Y$ be a standard Brownian motion independent of $X$. Fractional Brownian motion in Brownian motion time (of index $H$), recently studied in…
This paper aims to provide a consistent, finite-valued, and mathematically well-defined reformulation of the Feynman path-integral measure for quantum fields obtained by studying the Wiener stochastic process in the infinite-dimensional…
Stochastic calculus with respect to fractional Brownian motion (fBm) has attracted a lot of interest in recent years, motivated in particular by applications in finance and Internet traffic modeling. Multifractional Brownian motion (mBm) is…
For the standard Quantum Brownian Motion (QBM) model, we point out the occurrence of simultaneous (parallel), mutually irreducible and autonomous decoherence processes. Besides the standard, one Brownian particle, we show there is at least…
Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einstein's theory of Brownian motion, however, is only applicable at long time scales. At short…
The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed in the probabilistic literature, in comparison with the quarter plane analogue model. In this context, our main result is to prove that the…
We consider quantum Hamiltonian systems composed of mutually interacting "dynamical subsystem" with one or several degrees of freedom and "thermostat" with arbitrary many degrees of freedom, under assumptions that the interaction ensures…
We study the motion of an inertial particle in a fractional Gaussian random field. The motion of the particle is described by Newton's second law, where the force is proportional to the difference between a background fluid velocity and the…
A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…
Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional formalism of quantum mechanics, using a path-integral description. This is done explicitly for the case of a…
The classical motion of spinning particles can be described without employing Grassmann variables or Clifford algebras, but simply by generalizing the usual spinless theory. We only assume the invariance with respect to the Poincare' group;…
We extend to any dimension the quantitative fourth moment theorem on the Poisson setting, recently proved by C. D\"obler and G. Peccati (2017). In particular, by adapting the exchangeable pairs couplings construction introduced by I.…
The approach to the theory of a relativistic random process is considered by the path integral method as Brownian motion taking into account the boundedness of speed. An attempt was made to build a relativistic analogue of the Wiener…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
We prove a bound for the Wasserstein distance between vectors of smooth complex random variables and complex Gaussians in the framework of complex Markov diffusion generators. For the special case of chaotic eigenfunctions, this bound can…
We show that in the presence of the torsion tensor $S^k_{\phantom{k}ij}$, the quantum commutation relation for the four-momentum, traced over spinor indices, is given by $[p_i,p_j]=2i\hbar S^k_{\phantom{k}ij}p_k$. In the Einstein--Cartan…
The free positive multiplicative Brownian motion $(h_t)_{t\geq0}$ is the large $N$ limit in non-commutative distribution of matrix geometric Brownian motion. It can be constructed by setting $h_t:=g_{t/2}g_{t/2}^*$, where $(g_t)_{t\geq0}$…
In Ayache and Taqqu (2005), the multifractional Brownian (mBm) motion is obtained by replacing the constant parameter $H$ of the fractional Brownian motion (fBm) by a smooth enough functional parameter $H(.)$ depending on the time $t$.…
We discuss chains of interacting Brownian motions. Their time reversal invariance is broken because of asymmetry in the interaction strength between left and right neighbor. In the limit of a very steep and short range potential one arrives…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…