Related papers: Onsager-Machlup action functional for stochastic p…
In this article, the path independent property of additive functionals of McKean-Vlasov stochastic differential equations with jumps is characterised by nonlinear partial integro-differential equations involving $L$-derivatives with respect…
For sampling multiple pathways in a rugged energy landscape, we propose a novel action-based path sampling method using the Onsager-Machlup action functional. Inspired by the Fourier-path integral simulation of a quantum mechanical system,…
We present a method to infer the arbitrary space-dependent drift and diffusion of a nonlinear stochastic model driven by multiplicative fractional Gaussian noise from a single trajectory. Our method, fractional Onsager-Machlup optimisation…
Many natural systems exhibit phase transition where external environmental conditions spark a shift to a new and sometimes quite different state. Therefore, detecting the behavior of a stochastic dynamic system such as the most probable…
The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian L\'evy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian…
The problem of estimating small transition probabilities for overdamped Langevin dynamics is considered. A simplification of Girsanov's formula is obtained in which the relationship between the infinitesimal generator of the underlying…
We first state a special type of It\^o formula involving stochastic integrals of both standard and fractional Brownian motions. Then we use Doss-Sussman transformation to establish the link between backward doubly stochastic differential…
The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a probabilistic representation of the Laplace transform of…
The main result of this article regards a small time approximation for the Girsanov's exponential. We prove that the latter is well described over short time intervals by the solution of a deterministic partial differential equation.The…
In this paper we extend models for the dynamic of the temperatures by considering random switching between Levy noises instead of Brownian motions, with a mean-reverting movement towards a seasonal periodic function. The use of Levy noises…
In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these…
Yet another proof of Onsager-Machlup formula for diffusion processes on a Riemannian manifold after Takahashi-Watanabe, Fujita-Kotani. The proof is purely probabilistic and contains a precise study on an ergodic effect for a key Wiener…
In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractional Brownian motion. We firstly derive the pathwise spatial and temporal regularity of the generalized Ornstein-Uhlenbeck…
Extracting governing stochastic differential equation models from elusive data is crucial to understand and forecast dynamics for complex systems. We devise a method to extract the drift term and estimate the diffusion coefficient of a…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
By using a simple observation that the density processes appearing in Ito's martingale representation theorem are invariant under the change of measures, we establish a non-linear version of the Cameron-Martin formula for solutions of a…
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining…
Stochastic integration with respect to Gaussian processes, such as fractional Brownian motion (fBm) or multifractional Brownian motion (mBm), has raised strong interest in recent years, motivated in particular by applications in finance,…
This is an overview about natural sample spaces for differential equations driven by various noises. Appropriate sample spaces are needed in order to facilitate a random dynamical systems approach for stochastic differential equations. The…
We introduce a new method for analyzing midpoint discretizations of stochastic differential equations (SDEs), which are frequently used in Markov chain Monte Carlo (MCMC) methods for sampling from a target measure $\pi \propto \exp(-V)$.…