相关论文: On pathwise uniform approximation of processes wit…

We consider the class of stationary-increment harmonizable stable processes with infinite control measure, which most notably includes real harmonizable fractional stable motions. We give conditions for the integrability of the paths of…

The calculation of the decay rate of a metastable state in the path-integral formulation of stochastic processes is revisited. Previous derivations of this rate were achieved at the cost of a step that is difficult to justify…

We define and investigate the properties of the jaggedness of path integral trajectories. The new quantity is shown to be scale invariant and to satisfy a self-averaging property. Jaggedness allows for a classification of path integral…

We establish a universal approximation theorem for signatures of rough paths that are not necessarily weakly geometric. By extending the path with time and its rough path bracket terms, we prove that linear functionals of the signature of…

The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous…

Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…

We to define a Path Integral in Lorentzian time by restricting the relevant domain of integration on $C([0,1],M)$ over a Riemannian configuration manifold $(M,g)$ and considering the dynamics of a particle evolving between to fixed…

In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…

The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The extremal range for a stochastic process is defined by limit…

This paper presents an identity between the multivariate and univariate saddlepoint approximations applied to sample path probabilities for a certain class of stochastic processes. This class, which we term the recursively compounded…

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…

We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational…

This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic…

Two problems are addressed for the path of certain stochastic processes: a) do they define currents? b) are these currents of a classical type? A general answer to question a) is given for processes like semimartingales or with Lyons-Zheng…

This paper contributes to the study of a new and remarkable family of stochastic processes that we will term class $\Sigma^{r}(H)$. This class is potentially interesting because it unifies the study of two known classes: the class…

We present a new framework for recycling independent variational approximations to Gaussian processes. The main contribution is the construction of variational ensembles given a dictionary of fitted Gaussian processes without revisiting any…

Dynamical processes can be classified in various ways as deterministic or stochastic, and continuous or discrete time. All these types can be studied by the path-spaces they generate, and stationary measures on that path-space. Such…

Stein's method for Gaussian process approximation can be used to bound the differences between the expectations of smooth functionals $h$ of a c\`adl\`ag random process $X$ of interest and the expectations of the same functionals of a well…

Stochastic symmetries and related invariance properties of finite dimensional SDEs driven by general c\`adl\`ag semimartingales taking values in Lie groups are defined and investigated. In order to enlarge the class of possible symmetries…

This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…