Related papers: A stochastic approach in physics exercises of math…
We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
It is becoming common to hear teaching advice about spending more time on the "physics of the problem" so that students will get more physical insight and develop a stronger intuition that can be very helpful when thinking about physics…
When learning skills from demonstrations, one is often required to think in advance about the appropriate task representation (usually in either operational or configuration space). We here propose a probabilistic approach for…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
A stochastic control of the vibrational motion for a single trapped ion/atom is proposed. It is based on the possibility to continously monitor the motion through a light field meter. The output from the measurement process should be then…
In this paper, we learn dynamics models for parametrized families of dynamical systems with varying properties. The dynamics models are formulated as stochastic processes conditioned on a latent context variable which is inferred from…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
This paper extends the application of the stochastic variational method to noncentral interactions. Several examples are presented for three- and four-nucleon systems with realistic nuclear forces. The correlated Gaussians easily cope with…
This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical…
By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…
This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…
In this work, multiplicative stochasticity is applied to the learning rate of stochastic optimization algorithms, giving rise to stochastic learning-rate schemes. In-expectation theoretical convergence results of Stochastic Gradient Descent…
In this paper, a stochastic model with regime switching is developed for solar photo-voltaic (PV) power in order to provide short-term probabilistic forecasts. The proposed model for solar PV power is physics inspired and explicitly…
This paper develops a systematic parametric method for analyzing stochastic systems under volatility uncertainty within the $G$-expectation framework. Leveraging the dual representation of the $G$-expectation as a supremum over a family of…
Over the last decade, a series of applied mathematics papers have explored a type of inverse problem--called by a variety of names including "inverse sensitivity", "pushforward based inference", "consistent Bayesian inference", or…
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…
We analyzed the stochastic behavior of systems controlled by autocatalytic reaction A+X -> X+X. Assuming the distribution of reacting particles in the system volume to be uniform, we introduced the notion of the point model of reaction…
We show that a substantial portion of stochastic calculus can be developed along similar lines to ordinary calculus, with derivative-based concepts driving the development. We define a notion of stopping derivative, which is a form of right…