Related papers: Integration of rough paths - the truncated variati…

We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master…

We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…

When the one-form is $Lip\left(\gamma-1\right) $ with $\gamma >p\geq 1$, we construct the integral of a branched $p$-rough path, which defines another branched $p$-rough path. We derive a quantitative bound for this integral and prove that…

We derive an invariance principle for the lift to the rough path topology of stochastic processes with delayed regenerative increments under an optimal moment condition. An interesting feature of the result is the emergence of area anomaly,…

This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensitive with respect to noise. The integral invariant…

In this paper we provided a classification for partitions of intervals on the hyperbolic plane. Given a partition, to be named strong, we define a notion of a hyperbolic-valued functions of bounded variation and a kind of Riemann-Stieltjes…

Within path sampling framework, we show that probability distribution divergences, such as the Chernoff information, can be estimated via thermodynamic integration. The Boltzmann-Gibbs distribution pertaining to different Hamiltonians is…

Using a path integral approach, we derive an analytical solution of a nonlinear and singular Langevin equation, which has been introduced previously by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion of a solid…

We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effective dynamics solves a rough differential equation, which is…

For any real-valued stochastic process $X$ with c\'rdl\'rg paths we define non-empty family of processes which have locally finite total variation, have jumps of the same order as the process $X$ and uniformly approximate its paths on…

The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…

In this paper, we study reflected differential equations driven by continuous paths with finite $p$-variation ($1\le p<2$) and $p$-rough paths ($2\le p<3$) on domains in Euclidean spaces whose boundaries may not be smooth. We define…

Path integrals developed by Richard Feynman have been an important tool in Physics in studying quantum field theory. In mathematics, it has also been widely used in providing formal proofs in the study of Index theorem and asymptotic…

In classical analysis, the relationship between continuity and Riemann integrability is an intimate one: a continuous function on a closed and bounded interval is always Riemann integrable whereas a Riemann integrable function is continuous…

Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, rough paths and related objects with a quantified singularity at zero. In a pure path…

In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our…

In line with the notion of probabilistic rough paths introduced in the previous contribution \cite{salkeld2021Probabilistic}, we address corresponding random controlled rough paths (first introduced in \cite{2019arXiv180205882.2B}), the…

In this paper we present an enhancement of the regression-based variance reduction approaches recently proposed in Belomestny et al. This enhancement is based on a truncation of the control variate and allows for a significant reduction of…

We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Ito isometry to Banach spaces. In the white noise case we obtain two…

We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory allowing to handle generalized integrals weighted by an exponential coefficient. The results are applied to the fractional…