相关论文: A converse to Pitman's theorem for a space-time Br…
We prove large deviations for $g(t)$-Brownian motion in a complete, evolving Riemannian manifold $M$ with respect to a collection $\{g(t)\}_{t\in [0,1]}$ of Riemannian metrics, smoothly depending on $t$. We show how the large deviations are…
We study the occupation fluctuations of drifted Brownian motion in a closed interval, and show that they undergo a dynamical phase transition in the long-time limit without an additional low-noise limit. This phase transition is similar to…
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 show that the random adjacency matrices induced by the chronological relations and i.i.d. samples of two spacetimes coincide in law if and only if the spacetimes in question are smoothly isometric. A similar result holds for weighted…
We prove an It\^o-Wentzell formula for the fractional Brownian motion. As an application we derive an existence and uniqueness result for a class of stochastic differential equations driven by this stochastic process.
In this note we consider generalized diffusion equations in which the diffusivity coefficient is not necessarily constant in time, but instead it solves a nonlinear fractional differential equation involving fractional Riemann-Liouville…
In order to overcome ambiguity problem on identification of mathematical objects in noncommutative theory with physical observables, quantum mechanical system coupled to the NC U(1) gauge field in the noncommutative space is reformulated by…
The inverse problem of fractional Brownian motion and other Gaussian processes with stationary increments involves inverting an infinite hermitian positively definite Toeplitz matrix (a matrix that has equal elements along its diagonals).…
We develop a quantization scheme for the quantum theory of a real scalar field on a class of non-commutative spacetime models collectively known as T-Minkowski. Requiring the theory to be covariant under T-Poincar\'e transformations, we…
We obtain a formula for the density of the winding number of planar Brownian motion around the origin, and deduce from it asymptotic expansions in inverse powers of the logarithm of the squared time, explicit in the angular variable. In…
In this paper we consider a class of time-dependent neutral stochastic functional differential equations with finite delay driven by a fractional Brownian motion in a Hilbert space. We prove an existence and uniqueness result for the mild…
We obtain some integrability properties and some limit theorems for the exit time from a cone of a planar Brownian motion, and we check that our computations are correct via Bougerol's identity.
This paper proves an equality in law between the invariant measure of a reflected system of Brownian motions and a vector of point-to-line last passage percolation times in a discrete random environment. A consequence describes the…
It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying $\text{Newton's}$ methods in $\textit{Principia}$ is neo-Newtonian or Galilean space-time. I…
A possible mechanism leading to anomalous diffusion is the presence of long-range correlations in time between the displacements of the particles. Fractional Brownian motion, a non-Markovian self-similar Gaussian process with stationary…
We revisit the Markov approximation necessary to derive ordinary Brownian motion from a model widely adopted in literature for this specific purpose. We show that this leads to internal inconsistencies, thereby implying that further search…
Consider a sequence of n bi-infinite and stationary Brownian queues in tandem. Assume that the arrival process entering in the first queue is a zero mean ergodic process. We prove that the departure process from the n-th queue converges in…
We propose a new wiew on the structure of quantum mechanics and postulate a q-deformed algebra of observables. We find equations of motion for this system, which guarantee a unitary time developement. We solve this equations for simple…
Reflected Brownian motion (RBM) in a wedge is a 2-dimensional stochastic process Z whose state space in R^2 is given in polar coordinates by S={(r,theta): r >= 0, 0 <= theta <= xi} for some 0 < xi < 2 pi. Let alpha= (theta_1+theta_2)/xi,…
We investigate first and second order fluctuations of additive functionals of a fractional Brownian motion (fBm) of the form \begin{align}\label{eq:abstractmain} Z_n=\left\{\int_{0}^{t}f(n^{H}(B_{s}-\lambda))ds\ ; t\geq 0 \right\}…