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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 consider a multiscale system of stochastic differential equations in which the slow component is perturbed by a small fractional Brownian motion with Hurst index $H>1/2$ and the fast component is driven by an independent Brownian motion.…

This paper is dedicated to the investigation of the asymptotic behavior of a delayed wave equation without the presence of any position term. First, it is shown that the problem is well-posed in the sense of semigroups theory. Thereafter,…

This work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic…

We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…

This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…

This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pertubed linear differential equations obey certain growth or…

In this paper we continue our work on adaptive timestep control for weakly non- stationary problems. The core of the method is a space-time splitting of adjoint error representations for target functionals due to S\"uli and Hartmann. The…

In [12] we formulated an evolutionary game theory model as a dynamical system on the state space of finite signed Borel measures under the weak* topology. The focus of this paper is to extend the analysis to include the long-time behavior…

We consider a class of cubic stochastic operators that are motivated by models for evolution of frequencies of genetic types in populations. We take populations with three mutually exclusive genetic types. The long term dynamics of single…

A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimental findings on behaviour of locusts. It exhibits nontrivial…

A class of evolution quasistatic systems which leads, after a suitable time discretization, to recursive nonlinear programs, is considered and optimal control or identification problems governed by such systems are investigated. The…

Non-smooth dynamics driven by stochastic disturbance arise in a wide variety of engineering problems. Impulsive interventions are often employed to control stochastic systems; however, the modeling and analysis subject to execution delay…

We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…

Existing analysis of AdaGrad and other adaptive methods for smooth convex optimization is typically for functions with bounded domain diameter. In unconstrained problems, previous works guarantee an asymptotic convergence rate without an…

In multivariate regression estimation, the rate of convergence depends on the dimension of the regressor. This fact, known as the curse of the dimensionality, motivated several works. The additive model, introduced by Stone (10), offers an…

Model-based Reinforcement Learning and Control have demonstrated great potential in various sequential decision making problem domains, including in robotics settings. However, real-world robotics systems often present challenges that limit…

Motivated by applications in economics and finance, in particular to the modeling of limit order books, we study a class of stochastic second-order PDEs with non-linear Stefan-type boundary interaction. To solve the equation we transform…

This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…

We study the performance of asymptotic and approximate consensus algorithms under harsh environmental conditions. The asymptotic consensus problem requires a set of agents to repeatedly set their outputs such that the outputs converge to a…