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This paper focuses on the strong convergence of the truncated $\theta$-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate,…
We study invariance and monotonicity properties of Kunita-type stochastic differential equations in $\RR^d$ with delay. Our first result provides sufficient conditions for the invariance of closed subsets of $\RR^d$. Then we present a…
In this paper, we first investigate the well-posedness of a backward stochastic differential equation where the driver depends on the law of the solution conditioned to a common noise. Under standard assumptions, we show that existence and…
In this paper, we study the Poisson stability (in particular, stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, pseudo periodicity,…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…
We consider a possible application of the Wa\.zewski topological method to feedback control systems and to more general dynamical systems. We show how this method can be used to prove the impossibility of global stabilization in such…
We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel'ski\u{\i} cone compression-expansion type methodologies and Schauder-type ones. In particular we…
We propose and analyze the convergence of a novel stochastic forward-backward splitting algorithm for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued maximal monotone cocoercive operator. This…
We consider a class of nonlinear ordinary differential equations of the second order with parameters. We establish conditions for perturbations of the coefficients of the equation under which the zero solution is asymptotically stable.…
In this paper, we propose a new framework for solving a general dynamic optimal stopping problem without time consistency. A sophisticated solution is proposed and is well-defined for any time setting with general flows of objectives. A…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
A particle with spin 1/2 is investigated both in expanding and oscillating cosmological de Sitter models. It is shown that these space-time geometries admit existence of the non-relativistic limit in the covariant Dirac equation. Procedure…
In this paper, we propose practical normalized stochastic first-order methods with Polyak momentum, multi-extrapolated momentum, and recursive momentum for solving unconstrained optimization problems. These methods employ dynamically…
This paper considers the Poisson equation for general state-space Markov chains in continuous time. The main purpose of this paper is to present specific bounds for the solutions of the Poisson equation for general state-space Markov…
Extended phase space of an elementary (relativistic) system is introduced in the spirit of the Souriau's definition of the `space of motions' for such system. Our formulation is generally applicable to any homogeneous space-time (e.g. de…
Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…
The paper is dedicated to studying the problem of Poisson stability (in particular stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, Bohr almost automorphy, Birkhoff recurrence, almost recurrence in the sense of…
This paper is devoted to studying non-commensurate fractional order planar systems. Our contributions are to derive sufficient conditions for the global attractivity of non-trivial solutions to fractional-order inhomogeneous linear planar…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…
A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving $p$-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper…