Related papers: Spin coherent states and stochastic hybrid path in…
For any real-valued stochastic process $X$ with c\'rdl\'rg paths we define non-empty family of processes which have locally finite total variation, have jumps of the same order as the process $X$ and uniformly approximate its paths on…
Assuring safety in discrete time stochastic hybrid systems is particularly difficult when only noisy or incomplete observations of the state are available. We first review a formulation of the probabilistic safety problem under noisy hybrid…
We explore a class of hybrid (piecewise deterministic) systems characterized by a large number of individuals inhabiting an environment whose state is described by a set of continuous variables. We use analytical and numerical methods from…
Probabilistic and stochastic behavior are omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of fundamental properties of nature, uncertain environments, or simplifications to…
In this paper, we develop the formulation of the spin coherent state in real parameterization up to SU(5). The path integral in this representation of coherent state and its classical consequence are investigated. Using the resolution of…
We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…
Transition phenomena between metastable states play an important role in complex systems due to noisy fluctuations. In this paper, the physics informed neural networks (PINNs) are presented to compute the most probable transition pathway.…
By returning to the underlying discrete time formalism, we relate spurious results in coherent state path integral calculations to the high frequency structure of their propagators. We show how to modify the standard expressions for…
The behavior of the most probable values of the order parameter $x$ and the amplitude $\phi$ of conjugate force fluctuations is studied for a stochastic system with a colored multiplicative noise with absorbing states. The phase diagrams…
The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization…
This paper is concerned with synchronization of complex stochastic dynamical networks in the presence of noise and functional uncertainty. A probabilistic control method for adaptive synchronization is presented. All required probabilistic…
Stochastic systems have a control-theoretic interpretation in which noise plays the role of control. In the weak-noise limit, relevant at low temperatures or in large populations, this leads to a precise mathematical mapping: the most…
This paper develops a systematic treatment of monotonicity-based pathwise dualities for Markov processes taking values in partially ordered sets. We show that every Markov process that takes values in a finite partially ordered set and…
Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the system state itself. In this paper, we establish the pathwise…
Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely…
We present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales. The objective of this method is to derive from the original system a new stochastic differential equation…
Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a…
This work introduces a novel paradigm for solving optimal control problems for hybrid dynamical systems under uncertainties. Robotic systems having contact with the environment can be modeled as hybrid systems. Controller design for hybrid…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…