Related papers: Weak differentiability of Wiener functionals and o…
Using structures of Abstract Wiener Spaces, we define a fractional Brownian field indexed by a product space $(0,1/2] \times L^2(T,m)$, $(T,m)$ a separable measure space, where the first coordinate corresponds to the Hurst parameter of…
This work considers a type of slow-fast system, where the slow component is driven by fractional Brownian motion with H > 1/2 and the fast component is a Markovian stationary process. Our solution mapping is defined based on the…
The primary purpose of this paper is to study the Wiener-type regularity criteria for non-linear equations driven by integro-differential operators, whose model is the fractional $p-$Laplace equation. In doing so, with the help of tools…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
We consider exponential functionals of a multi-dimensional Brownian motion with drift, defined via a collection of linear functionals. We give a characterization of the Laplace transform of their joint law as the unique bounded solution, up…
We obtain the fluctuations for the occupation time of one-dimensional symmetric exclusion processes with speed change, where the transition rates (conductances) are driven by a general function W. The approach does not require sharp bounds…
The objective of this paper is to prove a functional weak invariance principle for a local time of a process of the form $X_{n}=\varphi\circ T^{n}$ where $\left(X,\mathcal{B},T,m\right)$ is a measure preserving system with a transfer…
Fractional (in time and in space) evolution equations defined on Dirichlet regular bounded open domains, driven by fractional integrated in time Gaussian spatiotemporal white noise, are considered here. Sufficient conditions for the…
We prove that if $f:\mathbb{R}\to\mathbb{R}$ is Lipschitz continuous, then for every $H\in(0,1/4]$ there exists a probability space on which we can construct a fractional Brownian motion $X$ with Hurst parameter $H$, together with a process…
In this work we present expansions of intersection local times of fractional Brownian motions in $\R^d$, for any dimension $d\geq 1$, with arbitrary Hurst coefficients in $(0,1)^d$. The expansions are in terms of Wick powers of white noises…
We develop the functional It\^o/path-dependent calculus with respect to fractional Brownian motion with Hurst parameter $H> \frac{1}{2}$. Firstly, two types of integrals are studied. The first type is Stratonovich integral, and the second…
Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important non-monotonic averaging functions being excluded from the theoretical…
Within the context of rough path analysis via fractional calculus, we show how variability can be used to prove the existence of integrals with respect to H\"older continuous multiplicative functionals in the case of Lipschitz coefficients…
We study a class of linear first and second order partial differential equations driven by weak geometric $p$-rough paths, and prove the existence of a unique solution for these equations. This solution depends continuously on the driving…
We are interested in existence of solutions to the $d$-dimensional equation \begin{equation*} X_t=x_0+\int_0^t b(X_s)ds + B_t, \end{equation*} where $B$ is a (fractional) Brownian motion with Hurst parameter $H\leqslant 1/2$ and $b$ is an…
The paper deals with projection estimators of the density of the stationary solution $X$ to a differential equation driven by the fractional Brownian motion under a dissipativity condition on the drift function. A model selection method is…
The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another…
We derive a higher-order asymptotic expansion of the conditional characteristic function of the increment of an It\^o semimartingale over a shrinking time interval. The spot characteristics of the It\^o semimartingale are allowed to have…
The aim of this paper is to analyse a WIS-stochastic differential equation driven by fractional Brownian motion with $H>\tfrac{1}{2}$. For this, we summarise the theory of fractional white noise and prove a fundamental $L^2$-estimate for…
In this paper we generalize constructions of non-commutative integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamiltonian actions on symplectic manifolds split…