Related papers: Weak differentiability of Wiener functionals and o…
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…
We develop a non-anticipating calculus of variations for functionals on a space of laws of continuous semi-martingales, which extends the classical one. We extend Hamilton's least action principle and Noether's theorem to this generalized…
The fundamental solution of a pseudo-differential equation for functions defined on the $d$-fold product of the $p$-adic numbers, $\mathbb{Q}_p$, induces an analogue of the Wiener process in $\mathbb{Q}_p^d$. As in the real setting, the…
A general technique is developed for calculating functional determinants of second-order differential operators with Dirichlet, periodic, and antiperiodic boundary conditions. As an example, we give simple formulas for a harmonic oscillator…
This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures…
It is well known that, under suitable regularity conditions, the normalized fractional process with fractional parameter $d$ converges weakly to fractional Brownian motion for $d>1/2$. We show that, for any non-negative integer $M$,…
A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…
In this paper we obtain a Wiener-Hopf type factorization for a real-valued arithmetic Brownian motion with time-dependent drift and volatility. To the best of our knowledge, this paper is the very first step towards realizing the objective…
We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are obtained by obtained by computing a directional derivative of the weak…
This work is devoted to averaging principle of a two-time-scale stochastic partial differential equation on a bounded interval $[0, l]$, where both the fast and slow components are directly perturbed by additive noises. Under some regular…
In this paper we localize some of Watanabe's results on fractional Wiener functionals, and use them to give a precise estimate of the difference between two Donsker's delta functionals even with fractional differentiability. As an…
In this paper we introduce the notion of fractional martingale as the fractional derivative of order $\alpha$ of a continuous local martingale, where $\alpha\in(-{1/2},{1/2})$, and we show that it has a nonzero finite variation of order…
In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional It\^o formula…
The center of interest in this work are variational problems with integral functionals depending on special nonlocal gradients. The latter correspond to truncated versions of the Riesz fractional gradient, as introduced in [Bellido, Cueto &…
We obtain well-posedness results for a class of ODE with a singular drift and additive fractional noise, whose right-hand-side involves some bounded variation terms depending on the solution. Examples of such equations are reflected…
The convergence of stochastic integrals driven by a sequence of Wiener processes $W_n\to W$ (with convergence in $C_t$) is crucial in the analysis of stochastic partial differential equations (SPDEs). The convergence we focus on in this…
Functionals that strive to correct for such self-interaction errors, such as those obtained by imposing the Perdew-Zunger self-interaction correction or the generalized Koopmans' condition, become orbital dependent or orbital-density…
The present work constitutes a first step towards establishing a systematic framework for treating variational problems that depend on a given input function through a mixture of its derivatives of different orders in different directions.…
The Wiener's path integral plays a central role in the studies of Brownian motion. Here we derive exact path-integral representations for the more general \emph{fractional} Brownian motion (fBm) and for its time derivative process -- the…
Quadratic fluctuations require an evaluation of ratios of functional determinants of second-order differential operators. We relate these ratios to the Green functions of the operators for Dirichlet, periodic and antiperiodic boundary…