Showing papers in "Stochastic Processes and their Applications in 2020"

TL;DR: In this article, the central limit theorem for neural networks with a single hidden layer was proved in the asymptotic regime of simultaneously (a) large numbers of hidden units and (b) large number of stochastic gradient descent training iterations.

TL;DR: In this paper, the authors prove pathwise uniqueness for stochastic systems of McKean-Vlasov type with singular drift, even in the measure argument, and uniformly non-degenerate Lipschitz diffusion matrix.

TL;DR: In this paper, the selection problem of equilibria for a mean-field game without common noise was studied and a common approach was proposed to select, amongst all the equilibrics, those yielding the minimal cost for the representative player.

TL;DR: In this article, the authors consider the one-dimensional stochastic heat equation driven by a multiplicative space-time white noise and show that the spatial integral of the solution from − R to R converges in total variance distance to a standard normal distribution as R tends to infinity, after renormalization.

TL;DR: In this article, the weak differentiability of the unique strong solution with respect to the starting point x as well as Bismut-Elworthy-Li's derivative formula for the following stochastic differential equation in R d was shown.

TL;DR: In this paper, an averaging principle holds: the slow component converges to the solution of another semilinear, parabolic, SPDE, where the nonlinearity is averaged with respect to the invariant distribution of the fast process.

TL;DR: In this paper, the relation between nonlinear Levy processes and nonlinear Markovian convolution semigroups was studied under nonlinear expectations, nonlinear semigroup and fully nonlinear PDEs.

TL;DR: In this article, a game-theoretic framework for time-inconsistent stopping problems where the time inconsistency is due to the consideration of a non-linear function of an expected reward is developed.

TL;DR: In this paper, the optimal stopping problem with non-linear expectation (induced by a BSDE) is considered without making any regularity assumptions on the reward process, and the value family can be aggregated by an optional process.

TL;DR: In this paper, a general class of nonlinear stochastic differential equations with a hybrid switching diffusion is studied and a complete characterization of the asymptotic behavior of the system under consideration is provided.

TL;DR: In this article, the existence and uniqueness of mean square solutions to the equations are proved when the nonlinear drift and diffusion terms are locally Lipschitz continuous and it is shown that the mean random dynamical system generated by the solution operators has a unique tempered weak pullback random attractor in a Bochner space.

TL;DR: In this paper, a multidimensional random walk conditioned to stay in a cone is shown to have functional convergence towards the Brownian meander in the cone and functional convergence to the corresponding h -transform of the motion.

TL;DR: In this paper, the convergence rate of the Central Limit Theorem under sublinear expectations was studied. But the convergence of the central limit theorem under a sublinear expectation was not studied.

TL;DR: In this paper, the authors study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space.

TL;DR: In this paper, the authors studied weighted distances in scale-free spatial network models: hyperbolic random graphs, geometric inhomogeneous random graphs and scale free percolation, and showed that typical distances within the giant/infinite component converge in distribution.

TL;DR: A pathwise proof of the HWI inequality which is based on en-tropic interpolations rather than displacement ones, which is closer to the Otto-Villani heuristics than the original rigorous proof presented in the second part of [23].

TL;DR: In this article, the authors considered the two-dimensional stochastic damped nonlinear wave equation (SdNLW) with the cubic nonlinearity, forced by a space-time white noise.

TL;DR: It is proved that the nested distance of processes generates a Polish topology but is itself not a complete metric, and its completion is identified to be the set of nested distributions, which are a form of generalized stochastic processes.

TL;DR: In this paper, the authors introduced the notion of left-monotone transports, which are characterized equivalently by a no-crossing property of their support, as simultaneous optimizers for a class of bivariate transport cost functions with a Spence-Mirrlees property and by an order-theoretic minimality property.

TL;DR: In this article, the authors investigate the well-posedness of backward or forward stochastic differential equations whose law is constrained to live in an a priori given (smooth enough) set and which is reflected along the corresponding normal vector.

TL;DR: In this paper, a stochastic search model with resetting for an unknown stationary target with known distribution was considered, and the authors obtained quantitative growth rates for the search process as a function of the rate function.

TL;DR: In this paper, the authors study the long time behavior of the solution to some McKean-Vlasov stochastic differential equation (SDE) driven by a Poisson process and prove that for a small enough interaction parameter, any solution converges to the unique (in this case) invariant measure.

TL;DR: By means of Malliavin calculus, it is proved that the backward Euler scheme applied to this auxiliary equation ensures the positivity of the numerical solution, and is of strong order one.

TL;DR: This paper focuses on convergence of the joint empirical measure for in- and out-degrees and proves the consistency of the Hill estimator.

TL;DR: In this paper, the authors derive a stochastic representation of the solution to a nonlocal-in-time evolution equation with a historical initial condition, which serves a bridge between normal diffusion and anomalous diffusion.

TL;DR: In this article, the error estimates in Peng's central limit theorem for not necessarily nondegenerate case are given for the one-dimensional case, where the authors use the language of classical probability theory instead of the theory of sublinear expectations.

TL;DR: In this article, a large class of symmetric pure jump Markov processes dominated by isotropic unimodal Levy processes with weak scaling conditions was considered and sharp two-sided heat kernel estimates for these processes were obtained in C 1, 1 open sets.

TL;DR: In this article, a different explicit full-discrete scheme was proposed to numerically solve the stochastic Allen-Cahn equation with cubic nonlinearity, perturbed by additive space-time white noise.

TL;DR: In this paper, the authors relax the criterion of the Peskun type covariance ordering by considering two different invariant probabilities, and obtain, in place of a strict ordering of asymptotic variances, a bound of the importance sampling (IS) estimator by that of the direct MCMC.

TL;DR: Estimates of the difference between the nth step distributions of the perturbed MCwM and the unperturbed MH chains are shown, based on novel perturbation results for Markov chains which are of interest beyond theMCwM setting.