Related papers: On weak convergence for stochastic evolutionary sy…
We prove existence of weak solutions (in the probabilistic sense) for a general class of stochastic semilinear wave equations on bounded domains of $R^d$ driven by a possibly discontinuous square integrable martingale.
Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give…
Typically, a stochastic model relates stochastic "inputs" and, perhaps, controls to stochastic "outputs". A general version of the Yamada-Watanabe and Engelbert theorems relating existence and uniqueness of weak and strong solutions of…
We develop a general framework for the analysis of approximations to stochastic scalar conservation laws. Our aim is to prove, under minimal consistency properties and bounds, that such approximations are converging to the solution to a…
A Milstein-type scheme was proposed to improve the rate of convergence of its approximation of the solution to a stochastic differential equation driven by a vector of continuous semimartingales. A necessary and sufficient condition was…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
We prove a weak iterated invariance principle for a large class of non-uniformly expanding random dynamical systems. In addition, we give a quenched homogenization result for fast-slow systems in the case when the fast component corresponds…
For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first…
We propose a new weak convergence theorem for martingales, under gentler conditions than the usual convergence in probability of the sequence of associated quadratic variations. Its proof requires the combined use of Skorohod's…
In this paper, we investigate the weak convergence rate of Euler-Maruyama's approximation for stochastic differential equations with irregular drifts. Explicit weak convergence rates are presented if drifts satisfy an integrability…
In this paper, a systematic approach of constructing modified equations for weak stochastic symplectic methods of stochastic Hamiltonian systems is given via using the generating functions of the stochastic symplectic methods. This approach…
Using the weak convergence approach, we prove the large deviation principle (LDP) for solutions to quasilinear stochastic evolution equations with small Gaussian noise in the critical variational setting, a recently developed general…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
In order to accommodate the empirical fact that population structures are rarely simple, modern studies of evolutionary dynamics allow for complicated and highly-heterogeneous spatial structures. As a result, one of the most difficult…
This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
We study the asymptotic behavior of almost-orbits of abstract evolution systems in Banach spaces with or without a Lipschitz assumption. In particular, we establish convergence, convergence in average and almost-convergence of almost-orbits…
In this paper, we propose an Anderson-accelerated stochastic extragradient algorithm for solving a class of stochastic variational inequalities, by incorporating Anderson acceleration into the stochastic extragradient method under a…
This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the…
We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, but instead receive samples that are coupled over time. We show that as long as…