相关论文: A maximum principle for the stochastic differentia…

A refined version of the strong maximum principle is proven for a class of second order ordinary differential equations with possibly discontinuous non-monotone nonlinearities. Then, exploiting this tool, some optimal regularity results…

We prove a stochastic maximum principle for a control problem where the state equation is delayed both in the state and in the control, and also the final cost functional may depend on the past trajectories. The adjoint equations turn out…

The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of…

An analytical formula for the occurence probability of Markovian stochastic paths with repeatedly visited and/or equal departure rates is derived. This formula is essential for an efficient investigation of the trajectories belonging to…

We construct variations for the classes of regular solutions to degenerate Beltrami equations with restrictions of the set-theoretic type for the complex coefficient. On this basis, we prove the variational maximum principle and other…

In this paper we analyse the pathwise approximation of stochastic differential equations by polynomial splines with free knots. The pathwise distance between the solution and its approximation is measured globally on the unit interval in…

We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally…

In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in…

This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in…

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…

SDE's must be solved in the "anti-Ito" sense when their coefficients are independent. While the "noise-induced drift" matters for the sample paths, it is absent in the Fokker-Planck equation, which takes a particularly simple form and is…

Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…

We provide a very brief introduction to typical paths and the corresponding It\^o type integration. Relying on this robust It\^o integration, we prove an existence and uniqueness result for one-dimensional differential equations driven by…

The following optimization problem is considered. For a linear vector Ito equation. it is required to find an optimal deterministic control vector which minimizes a quadratic the functional. A necessary and sufficient condition for the…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

In this paper, we develop low regularity theory for 3D Burgers equation perturbed by a linear multiplicative stochastic force. This method is new and essentially different from the deterministic partial differential equations(PDEs). Our…

This is an attempt to address diffusion phenomena from the point of view of information theory. We imagine a regular hamiltonian system under the random perturbation of thermal (molecular) noise and chaotic instability. The irregularity of…

We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global…

A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…

Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with…