Related papers: Conformal Restriction and Brownian Motion
In this paper, employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderate deviation %(CLT for abbreviation) for a class of…
We construct a Bayesian sequential test of two simple hypotheses about the value of the unobservable drift coefficient of a Brownian motion, with a possibility to change the initial decision at subsequent moments of time for some penalty.…
We study the problem of parameter estimation for the homogenization limit of multiscale systems involving fractional dynamics. In the case of stochastic multiscale systems driven by Brownian motion, it has been shown that in order for the…
We show that the derivative of the intersection and self-intersection local times of alpha-stable processes are exponentially integrable for certain parameter values. This includes the Brownian motion case. We also discuss related results…
We study the relationship between mixed stochastic differential equations and the corresponding rough path equations driven by standard Brownian motion and fractional Brownian motion with Hurst parameter $H>1/2$. We establish a correction…
Let \ell be the projected intersection local time of two independent Brownian paths in R^d for d=2,3. We determine the lower tail of the random variable \ell(U), where U is the unit ball. The answer is given in terms of intersection…
It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays important…
This work presents higher order Lagrangian dynamics possessing locally conformal character. More concretely, locally conformal higher order Euler-Lagrange equations are written with particular focus on the second- and the third-order cases.
We study the problem of estimating a compact set $S\subset \mathbb{R}^d$ from a trajectory of a reflected Brownian motion in $S$ with reflections on the boundary of $S$. We establish consistency and rates of convergence for various…
We prove the convergence of $ \nN $-particle systems of Brownian particles with logarithmic interaction potentials onto a system described by the infinite-dimensional stochastic differential equation (ISDE). % For this proof we present two…
This paper describes joint work with Oded Schramm and Wendelin Werner establishing the values of the planar Brownian intersection exponents from which one derives the Hausdorff dimension of certain exceptional sets of planar Brownian…
The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion $B$ with Hurst index $H$. In the quadratic (resp. cubic) case, when $H<1/4$ (resp.…
We consider conformal defects with spins under the rotation group acting on the transverse directions. They are described in the embedding space formalism in a similar manner to spinning local operators, and their correlation functions with…
The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and…
We study some functional inequalities satisfied by the distribution of the solution of a stochastic differential equation driven by fractional Brownian motions. Such functional inequalities are obtained through new integration by parts…
This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and…
Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…
We derive general results on the small deviation behavior for some classes of iterated processes. This allows us, in particular, to calculate the rate of the small deviations for $n$-iterated Brownian motions and, more generally, for the…
The article contains a brief description on the study of conformal scalar curvature equations, and discusses selected topics and questions concerning the equations in open spaces.
Stochastic variational inequalities provide a unified treatment for stochastic differential equations living in a closed domain with normal reflection and (or) singular repellent drift. When the domain is a polyhedron, we prove that the…