Related papers: Integrable Ito equations with multiple noises
It is known that knowledge of a symmetry of a scalar Ito stochastic differential equations leads, thanks to the Kozlov substitution, to its integration. In the present paper we provide a classification of scalar autonomous Ito stochastic…
We provide a symmetry classification of scalar stochastic equations with multiplicative noise. These equations can be integrated by means of the Kozlov procedure, by passing to symmetry adapted variables.
Symmetries can be used to integrate scalar Ito equation -- or reduce systems of such equations -- by the Kozlov substitution, i.e. passing to symmetry adapted coordinates. While the theory is well established for so called deterministic…
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…
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…
We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Ito vs. Stratonovich), in particular in the context of noise-induced…
A free choice of the integration sense would lead to the paradox that the number of possible equations (thus of solutions for a given model) can vary under a mere change of the variables. This is shown by a specific change which neutralizes…
An Ito-Skorokhod bi-linear equation driven by infinitely many independent colored noises is considered in a normal triple of Hilbert spaces. The special feature of the equation is the appearance of the Wick product in the definition of the…
It is shown that a generalized Ito system of four coupled nonlinear evolution equations passes the Painleve test for integrability in five distinct cases, of which two were introduced recently by Tam, Hu and Wang. A conjecture is formulated…
Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point differential-difference equations. This subclass includes…
This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations,…
We are concerned with the three dimensional navier-stokes equations driven by a general multiplicative noise. For every divergence free and mean free initial condition in L2, we establish existence of infinitely many global-in-time…
This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continuous. A characteristic property of this class of equations,…
We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder - diversity of intrinsic oscillatory frequencies and external independent noise.…
A simple axiomatic characterization of the noncommutative Ito algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that every quotient Ito algebra has a faithful representation in a…
We discuss W-symmetries of Ito stochastic differential equations, introduced in a recent paper by Gaeta and Spadaro [J. Math. Phys. 2017]. In particular, we discuss the general form of acceptable generators for continuous (Lie-point)…
The Ito-Stratonovich dilemma is revisited from the perspective of the interpretation of Stratonovich calculus using shot noise. Over the long time scales of the displacement of an observable, the principal issue is how to deal with…
The main objective of this work is to investigate the integrability and linearizability problems around a singular point at the origin of the family of differential systems Particularly we are interested in the three-dimensional cubic…
The finite sample properties of estimators are usually understood or approximated using asymptotic theories. Two main asymptotic constructions have been used to characterize the presence of many instruments. The first assumes that the…
In this paper, we present a pathwise construction of multi-soliton solutions for focusing stochastic nonlinear Schr\"odinger equations with linear multiplicative noise, in both the $L^2$-critical and subcritical cases. The constructed…