Related papers: Effective Langevin equations for constrained stoch…
This paper is concerned with the Fokker-Planck (FP) description of classical stochastic systems with discrete time delay. The non-Markovian character of the corresponding Langevin dynamics naturally leads to a coupled infinite hierarchy of…
Recently found positive representation for an arbitrary complex, gaussian weight is used to construct a statistical formulation of gaussian path integrals directly in the Minkowski time. The positivity of Minkowski weights is achieved by…
The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…
Brownian simulations can be used to generate statistics relevant for studying molecular interactions or trafficking. However, the concurrent simulation of many Brownian trajectories at can become computationally intractable. Replacing…
We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for…
We obtain explicit solutions for the density $\varphi_T$ of the first-time $T$ that a one-dimensional Brownian process $B$ reaches the twice, continuously differentiable moving boundary $f$ and such that $f''(t)\geq 0$ for all $t\in…
Inspired by the recent work of Bertini and Posta, who introduced the boundary driven Brownian gas on $[0,1]$, we study boundary driven systems of independent particles in a general setting, including particles jumping on finite graphs and…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
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…
Use energy-based model for bridge-type innovation. The loss function is explained by the game theory, the logic is clear and the formula is simple and clear. Thus avoid the use of maximum likelihood estimation to explain the loss function…
A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work,…
We generalize the notion of Gaussian bridges by conditioning Gaussian processes given that certain linear functionals of the sample paths vanish. We show the equivalence of the laws of the unconditioned and the conditioned process and by an…
This paper is devoted to a system of stochastic partial differential equations (SPDEs) that have a slow component driven by fractional Brownian motion (fBm) with the Hurst parameter $H >1/2$ and a fast component driven by fast-varying…
We demonstrate that a Langevin equation that describes the motion of a Brownian particle under non-equilibrium conditions can be exactly transformed to a special equation that explicitly exhibits the response of the velocity to a time…
We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process (not necessarily a semi-martingale). No adaptedness of initial point or vector fields is assumed. Under a simple condition on the…
Numerical methods for stochastic partial differential equations typically estimate moments of the solution from sampled paths. Instead, we shall directly target the deterministic equations satisfied by the first and second moments, as well…
The critical step in a molecular process is often a rare-event and has to be simulated by an enhanced sampling protocol. Recovering accurate dynamical estimates from such biased simulation is challenging. Girsanov reweighting is a method to…
We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of…