相关论文: Asymptotic symmetry and asymptotic solutions to It…

Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…

We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…

We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart…

Symmetry methods are by now recognized as one of the main tools to attack deterministic differential equations (both ODEs and PDEs); the situation is quite different for what concerns stochastic differential equations: here, symmetry…

It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…

This paper addresses the problem of stabilizing a part of variables for control systems described by stochastic differential equations of the Ito type. The considered problem is related to the asymptotic stability property of invariant sets…

Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…

We study the invariance of stochastic differential equations under random diffeomorphisms, and establish the determining equations for random Lie-point symmetries of stochastic differential equations, both in Ito and in Stratonovich form.…

This paper considers the asymptotic behaviour of deterministically and stochastically forced linear pantograph equations. The asymptotic behaviour is studied in the case when all solutions of the pantograph equation without forcing tend to…

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…

Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…

The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…

We discuss the interrelations between symmetry of an Ito stochastic differential equations (or systems thereof) and its integrability, extending in party results by R. Kozlov [J. Phys. A ${\bf 43}$ (2010) \& ${\bf 44}$ (2011)]. Together…

Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…

The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…

We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and…

In the deterministic realm, both differential equations and symmetry generators are geometrical objects, and behave properly under changes of coordinates; actually this property is essential to make symmetry analysis independent of the…

This paper features and elaborates recent developments and modifications in asymptotic techniques in solving differential equation in non linear dynamics. These methods are proved to be powerful to solve weakly as well as strongly non…

We study some properties concerning the asymptotic behavior of solutions to nonautonomous retarded functional differential equations, depending on the knowledge of certain solutions of the associated generalized characteristic equation.

The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e.,…