Abstract. In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere stochastic (invertible) flow associated with the SDE in the sense of Lebesgue measure. In the case of constant diffusions and BV drifts, we obtain such ...

We are interested in stationary “fluid” random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels. In an intermediate phase, for which there exists a coalesc...

Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this appr...

Stochastic differential equation (SDE) models offer one formulation for introducing uncertainty in human interactions in a dynamic social network model based on static and/or deterministic ordinary differential equation (ODE) models. A coupled SDE system for agent characteristics and connectivities was developed and investigated in [4]. This SDE model (which tacitly assumed instantaneous influe...

We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising for instance in finance and economics. The underlying process is a strong solution of one-dimensional, time-homogeneous stochastic differential equation (SDE). The proof relies on both analytic and probabilistic arguments and it is based on a contradict...

This paper explores the reconstruction of drift or diffusion coefficients of a scalar stochastic diffusion processes as it starts from an initial value and reaches, for the first time, a threshold value. We show that the distribution function derived from repeated measurements of the first-exit times can be used to formally partially reconstruct the dynamics of the process. Upon mapping the rel...

Perturbations to Markov chains and Markov processes are considered. The unperturbed problem is assumed to be geometrically ergodic in the sense usually established through the use of Foster–Lyapunov drift conditions. The perturbations are assumed to be uniform, in a weak sense, on bounded time intervals. The long-time behavior of the perturbed chain is studied. Applications are given to numeric...

Modeling noise in filtering problems is often done by means of stochastic differential equations (sde) driven by Brownian motion. The signal is thus a Markov process and, in particular, a diffusion process under general regularity assumptions. However, practical engineering problems requiring filtering often start as deterministic systems. Hence the problem of “imbedding” a deterministic system...

It is well-known that a stochastic differential equation (SDE) on a Euclidean space driven by a Brownian motion with Lipschitz coefficients generates a stochastic flow of homeomorphisms. When the coefficients are only locally Lipschitz, then a maximal continuous flow still exists but explosion in finite time may occur. If – in addition – the coefficients grow at most linearly, then this flow ha...

Stability is the most relevant property of dynamical systems. The stability stochastic differential equations a challenging and still open problem. In this article, using fuzzy Mittag–Leffler function, we introduce new controller function to stabilize equation (SDE) ν′(γ,μ)=Fγ,μ,ν(γ,μ). By adopting fixed point technique, are able prove Mittag–Leffler–Hyers–Ulam–Rassias SDE.