Related papers: Most probable flows for Kunita SDEs
This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric $\alpha$-stable L\'{e}vy motion ($0<\alpha<1$) or Brownian motion. For stochastic dynamical systems…
In this paper we prove, for small Hurst parameters, the higher order differentiability of a stochastic flow associated with a stochastic differential equation driven by an additive multi-dimensional fractional Brownian noise, where the…
We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood…
We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the…
Stochastic processes of evolving shapes are used in applications including evolutionary biology, where morphology changes stochastically as a function of evolutionary processes. Due to the non-linear and often infinite-dimensional nature of…
Brownian motion on manifolds with non-trivial diffusion coefficient can be constructed by stochastic development of Euclidean Brownian motions using the fiber bundle of linear frames. We provide a comprehensive study of paths for such…
In this paper, we consider a stochastic model of incompressible second grade fluids on a bounded domain of R^2 driven by linear multiplicative Brownian noise with anticipating initial conditions. The existence and uniqueness of the…
A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…
The aim of these notes is to give an overview of the current results about existence and uniqueness of solutions for the stochastic Euler equation driven by a Brownian noise in a two-dimensional bounded domain.
We consider a linear stochastic differential equation with stochastic drift and multiplicative noise. We study the problem of approximating its solution with the process that solves the equation where the possibly stochastic drift is…
We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
We propose a method for developing the flows of stochastic dynamical systems, posed as Ito's stochastic differential equations, on a Riemannian manifold identified through a suitably constructed metric. The framework used for the stochastic…
Motivated by the probabilistic representation for solutions of the Navier-Stokes equations, we introduce a novel class of stochastic differential equations that depend on the entire flow of its time marginals. We establish the existence and…
Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…
We consider two related linear PDE's perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a…
This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…
The motion of weakly inertial Brownian particles, transported by steady two-dimensional fluid flows, is investigated by means of asymptotic methods. We focus on the phenomenon of noise-induced separatrix crossing, which can force particles…
This paper presents a heuristic derivation of a geometric minimum action method that can be used to determine most-probable transition paths in noise-driven dynamical systems. Particular attention is focused on systems that violate detailed…
We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index 0<H<1/2 and 1/2<H<1. Under some assumptions on the drift coefficient, we…