Master equations and the theory of stochastic path integrals

MF Weber, E Frey - Reports on Progress in Physics, 2017 - iopscience.iop.org
This review provides a pedagogic and self-contained introduction to master equations and
to their representation by path integrals. Since the 1930s, master equations have served as …

Colored noise in dynamical systems

P Häunggi, P Jung - Advances in chemical physics, 1994 - Wiley Online Library
The general subject of colored noise driven dynamical flows is rooted in the study of the
motion of small particles suspended in a fluid and moving under the influence of random …

A computable evolution equation for the joint response-excitation probability density function of stochastic dynamical systems

D Venturi, TP Sapsis, H Cho… - Proceedings of the …, 2012 - royalsocietypublishing.org
By using functional integral methods, we determine a computable evolution equation for the
joint response-excitation probability density function of a stochastic dynamical system driven …

Escape from a fluctuating double well

AJR Madureira, P Hänggi, V Buonomano… - Physical Review E, 1995 - APS
We study thermally driven escape from a double well over a fluctuating barrier height. The
fluctuations of the bistable potential are governed by exponentially correlated Gaussian …

Stochastic delay differential equations: Analysis and simulation studies

RC Kumaran, TG Venkatesh, KS Swarup - Chaos, Solitons & Fractals, 2022 - Elsevier
Stochastic delay differential equations play an important role in modelling scientific and
engineering systems. In this paper the partial differential equation satisfying the time …

Confined active particles with spatially dependent Lorentz force: an odd twist to the" best Fokker-Planck approximation"

R Wittmann, I Abdoli, A Sharma, JM Brader - arXiv preprint arXiv …, 2024 - arxiv.org
We derive a version of the so-called" best Fokker-Planck approximation"(BFPA) to describe
the spatial properties of interacting active Ornstein-Uhlenbeck particles (AOUPs) in arbitrary …

Mori-Zwanzig approach to uncertainty quantification

D Venturi, H Cho… - Handbook of uncertainty …, 2017 - asu.elsevierpure.com
Determining the statistical properties of nonlinear random systems is a problem of major
interest in many areas of physics and engineering. Even with recent theoretical and …

Stochastic analysis of time-variant nonlinear dynamic systems. Part 1: The Fokker-Planck-Kolmogorov equation approach in stochastic mechanics

SV Ulyanov, M Feng, VS Ulyanov, K Yamafuji… - Probabilistic …, 1998 - Elsevier
The probabilistic description and analysis of the response of time-invariant nonlinear
dynamic systems driven by stochastic processes is usually treated by means of evaluation of …

Hierarchies of Landau-Lifshitz-Bloch equations for nanomagnets: A functional integral framework

J Tranchida, P Thibaudeau, S Nicolis - Physical Review E, 2018 - APS
We propose a functional integral framework for the derivation of hierarchies of Landau-
Lifshitz-Bloch (LLB) equations that describe the flow toward equilibrium of the first and …

Damped bistable system driven by colored noise: A digital simulation study

C Mahanta, TG Venkatesh - Physical Review E, 1998 - APS
We present digital computer simulation results of stochastic differential equations associated
with a damped bistable potential. The mean first passage time (MFPT) and the stationary …