Related papers: The Edwards Model for fBm Loops and Starbursts
A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility. We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel…
We consider stochastic integration with respect to fractional Brownian motion (fBm) with $H < 1/2$. The integral is constructed as the limit, where it exists, of a sequence of Riemann sums. A theorem by Gradinaru, Nourdin, Russo & Vallois…
Brownian motion and viscoelasticity of semiflexible polymers is a subject that has been studied for many years. Still, rigorous analysis has been hindered due to the difficulty in handling the constraint that polymer chains cannot be…
The model of Brownian Percolation has been introduced as an approximation of discrete last-passage percolation models close to the axis. It allowed to compute some explicit limits and prove fluctuation theorems for these, based on the…
We characterize the multifractal behavior of Brownian motion in the vicinity of an absorbing star polymer. We map the problem to an O(M)-symmetric phi^4-field theory relating higher moments of the Laplacian field of Brownian motion to…
Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions,…
There is much confusion in the literature over Hurst exponents. Recently, we took a step in the direction of eliminating some of the confusion. One purpose of this paper is to illustrate the difference between fBm on the one hand and…
It is well-known under the name of `periodic homogenization' that, under a centering condition of the drift, a periodic diffusion process on R^d converges, under diffusive rescaling, to a d-dimensional Brownian motion. Existing proofs of…
We study the pathwise regularity of the map $$ \phi \mapsto I(\phi) = \int_0^T < \phi(X_t), dX_t>$$ where $\phi$ is a vector function on $\R^d$ belonging to some Banach space $V$, $X$ is a stochastic process and the integral is some version…
Physisorption or chemisorption from dilute polymer solutions often entails irreversible polymer-surface bonding. We present a theory of the non-equilibrium layers which result. While the density profile and loop distribution are the same as…
This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the…
The density distribution function of the integral of the exponential Brownian motion is determined explicitly in the form of a rapidly convergent series.
In this note we prove the existence of a density for the law of the solution for 1-dimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter $H…
We construct magnetostatic models of coronal loops in which the thermodynamics of the loop is fully consistent with the shape and geometry of the loop. This is achieved by treating the loop as a thin, compact, magnetic fibril that is a…
While the theory of diffusion of a single Brownian particle in confined geometries is well-established by now, we discuss here the theoretical framework necessary to generalize the theory of diffusion to dense suspensions of strongly…
We consider a spring-block model with both dry and viscous frictions, subjected to a periodic driving allowing mechanically stable configurations to be sampled. We show that under strong driving, the scaling of the correlation length with…
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this…
We show that the longitudinal position $x(t)$ of a particle in a $(d+1)$-dimensional layered random velocity field (the Matheron-de Marsily model) can be identified as a fractional Brownian motion (fBm) characterized by a variable Hurst…
We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete observations of such dynamics in stationary…
We consider the active Brownian particle (ABP) model for a two-dimensional microswimmer with fixed speed, whose direction of swimming changes according to a Brownian process. The probability density for the swimmer evolves according to a…