Related papers: Stochastic integral representations and classifica…
In this paper, we give a new covariation spectral representation of some non stationary symmetric $\alpha$-stable processes (S$\alpha$S). This representation is based on a weaker covariation pseudo additivity condition which is more general…
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…
Stochastic integrals are defined with respect to a collection $P = (P_i; \, i \in I)$ of continuous semimartingales, imposing no assumptions on the index set $I$ and the subspace of $\mathbb{R}^I$ where $P$ takes values. The integrals are…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
For a strictly stationary sequence of $\mathbb{R}_{+}^{d}$--valued random vectors we derive functional convergence of partial maxima stochastic processes under joint regular variation and weak dependence conditions. The limit process is an…
It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal…
For each $n\geq 1$, let $ {X_{in}, \quad i \geq 1} $ be independent copies of a nonnegative continuous stochastic process $X_{n}=(X_n(t))_{t\in T}$ indexed by a compact metric space $T$. We are interested in the process of partial maxima…
We study integral representations of random variables with respect to general H\"older continuous processes and with respect to two particular cases; fractional Brownian motion and mixed fractional Brownian motion. We prove that arbitrary…
We consider the representation of the value of a class of optimal stopping problems of linear diffusions in a linearized form as an expected supremum of a known function. We establish an explicit integral representation of this representing…
Extreme-value theory for random vectors and stochastic processes with continuous trajectories is usually formulated for random objects all of whose univariate marginal distributions are identical. In the spirit of Sklar's theorem from…
Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…
Many aspects of the asymptotics of Plancherel distributed partitions have been studied in the past fifty years, in particular the limit shape, the distribution of the longest rows, connections with random matrix theory and characters of the…
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
In this work we introduce a theory of stochastic integration for operator-valued integrands with respect to some classes of cylindrical martingale-valued measures in Hilbert spaces. The integral is constructed via the radonification of…
This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and…
Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…
By applying Rohlin's result on the classification of homomorphisms of Lebesgue space, the random inertial manifold of a stochastic damped nonlinear wave equations with singular perturbation is proved to be approximated almost surely by that…