Related papers: Convex ordering for random vectors using predictab…
We describe a probabilistic model involving iterated Brownian motion for constructing a random chainable continuum. We show that this random continuum is indecomposable.
In this paper, we give an alternative proof of the fact that, when compounding a nonnegative probability distribution, convex ordering between the distributions of the number of summands implies convex ordering between the resulting…
We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. To this end, we introduce a new estimator that…
We introduce a numerical method for Brownian dynamics with position dependent diffusion tensor which is second order accurate for sampling the invariant measure while requiring only one force evaluation per timestep. Analysis of the…
We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic…
Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different…
Convex combinations of i.i.d. random variables without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger,…
We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…
Stochastic convex optimization, where the objective is the expectation of a random convex function, is an important and widely used method with numerous applications in machine learning, statistics, operations research and other areas. We…
Here we present well-posedness results for first order stochastic differential inclusions, more precisely for sweeping process with a stochastic perturbation. These results are provided in combining both deterministic sweeping process…
Biased Brownian motion of point-size particles in a three-dimensional tube with smoothly varying cross-section is investigated. In the fashion of our recent work [Martens et al., PRE 83,051135] we employ an asymptotic analysis to the…
In this paper, we study a class of multi-dimensional reflected backward stochastic differential equations when the noise is driven by a Brownian motion and an independent Poisson point process, and when the solution is forced to stay in a…
Learning high-dimensional distributions is often done with explicit likelihood modeling or implicit modeling via minimizing integral probability metrics (IPMs). In this paper, we expand this learning paradigm to stochastic orders, namely,…
We introduce a new dependence order, termed the conditional convex order, whose minimal and maximal elements characterize independence and perfect dependence. Moreover, it characterizes conditional independence, satisfies information…
Many results on the convex order in the literature were stated for random variables with finite mean. For instance, a fundamental result in dependence modeling is that the sum of a pair of random random variables is upper bounded in convex…
In this work, we establish some stochastic comparison results for multivariate skew-elliptical random vectors. These multivariate stochastic comparisons involve Hessian and increasing-Hessian orderings as well as many of their special…
Consider an multidimensional obliquely reflected Brownian motion in the positive orthant, or, more generally, in a convex polyhedral cone. We find sufficient conditions for existence of a stationary distribution and convergence to this…
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…
In this note - starting from $d$-dimensional (with $d>1$) fuzzy vectors - we prove Donsker's classical invariance principle. We consider a fuzzy random walk ${S^*_n}=X^*_1+\cdots+X^*_n,$ where $\{X^*_i\}_1^{\infty}$ is a sequence of…
We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the…