相关论文: Generalised Brownian Motion and Second Quantisatio…

Kaufman's dimension doubling theorem states that for a planar Brownian motion $\{\mathbf{B}(t): t\in [0,1]\}$ we have $$\mathbb{P}(\dim \mathbf{B}(A)=2\dim A \textrm{ for all } A\subset [0,1])=1,$$ where $\dim$ may denote both Hausdorff…

In this work we take a closer look at the algebraic-operator correspondence between the momentum space and the position space which defines the form of the canonical momentum operator in position space in Quantum Mechanics (QM). Starting…

By using Brownian motion and stochastic calculus, we establish a second main theorem for holomorphic curves into a projective subvariety $V\subset\mathbb P^n(\mathbb C)$ with an arbitrary family $\mathcal Q$ of $q$ hypersurfaces…

Let $\{b_H(t),t\in\mathbb{R}\}$ be the fractional Brownian motion with parameter $0<H<1$. When $1/2<H$, we consider diffusion equations of the type \[X(t)=c+\int_0^t\sigma\bigl(X(u)\bigr)\mathrm {d}b_H(u)+\int _0^t\mu\bigl(X(u)\bigr)\mathrm…

We study a gravitational action which is a linear combination of the Hilbert-Palatini term and a term quadratic in torsion and possessing local Poincare invariance. Although this action yields the same equations of motion as General…

We discuss the relationships between some classical representations of the fractional Brownian motion, as a stochastic integral with respect to a standard Brownian motion, or as a series of functions with independent Gaussian coefficients.…

Fractional Brownian motion is a non-Markovian Gaussian process indexed by the Hurst exponent $H\in [0,1]$, generalising standard Brownian motion to account for anomalous diffusion. Functionals of this process are important for practical…

We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space. This process is a generalization of the set-indexed Brownian motion, when the condition of independance is…

We consider a single Brownian particle in a spatially symmetric, periodic system far from thermal equilibrium. This setup can be readily realized experimentally. Upon application of an external static force F, the average particle velocity…

Consider a metric graph G with set of vertices V. Assume that for every vertex in V one is given a Wentzell boundary condition. It is shown how one can construct the paths of a Brownian motion on G such that its generator - viewed as an…

We consider the general gauge theory with a closed irreducible gauge algebra possessing the non-anomalous global (super)symmetry in the case when the gauge fixing procedure violates the global invariance of classical action. The theory is…

Combinatorial formulas for the moments of the Brownian motion on classical compact Lie groups are obtained. These expressions are deformations of formulas of B. Collins and P. \'Sniady for moments of the Haar measure and yield a proof of…

In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the…

In this paper, we consider an inference problem for an Ornstein-Uhlenbeck process driven by a general one-dimensional centered Gaussian process $(G_t)_{t\ge 0}$. The second order mixed partial derivative of the covariance function $ R(t,\,…

We consider classical particles coupled to the quantized electromagnetic field in the background of a spatially flat Robertson-Walker universe. We find that these particles typically undergo Brownian motion and acquire a non-zero mean…

The Chern-Weil topological theory is applied to a classical formulation of general relativity in four-dimensional spacetime. Einstein--Hilbert gravitational action is shown to be invariant with respect to a novel translation…

A general paradigm for describing classical (and semiclassical) gravity is presented. This approach brings to the centre-stage a holographic relationship between the bulk and surface terms in a general class of action functionals and…

We explore a generalisation of the L\'evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all…

We briefly review the problem of Brownian motion and describe some intriguing facets. The problem is first treated in its original form as enunciated by Einstein, Langevin, and others. Then, utilizing the problem of Brownian motion as a…

Fractional Brownian motion (fBm) is an experimentally-relevant, non-Markovian Gaussian stochastic process with long-ranged correlations between the increments, parametrised by the so-called Hurst exponent $H$; depending on its value the…