Related papers: Optimal Diffusion Processes
A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
Diffusion with stochastic resetting, instantaneous returns of a diffusing particle to a reference point, creates a stationary probability distribution. The paradigm is extended here to a doubly stochastic protocol in which the resetting…
Inspired by many examples in nature, stochastic resetting of random processes has been studied extensively in the past decade. In particular, various models of stochastic particle motion were considered where upon resetting the particle is…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
Unbalanced probability circulation, which yields cyclic motions in phase space, is the defining characteristics of a stationary diffusion process without detailed balance. In over-damped soft matter systems, such behavior is a hallmark of…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…
We consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is the variance of the filtered discrepancy process. The main contribution of this technical note is to show…
In this note, we discuss the uniform ergodicity of a diffusion process given by an It\^o stochastic differential equation. We present an integral condition in terms of the drift and diffusion coefficients that ensures the uniform ergodicity…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
This paper is concerned with the maximum principle and dynamic programming principle for mean-variance portfolio selection of jump diffusions and their relationship. First, the optimal portfolio and efficient frontier of the problem are…
We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…
In this article we derive Talagrand's $T_2$ inequality on the path space w.r.t. the maximum norm for various stochastic processes, including solutions of one-dimensional stochastic differential equations with measurable drifts, backward…
A general method is proposed which allows one to estimate drift and diffusion coefficients of a stochastic process governed by a Langevin equation. It extends a previously devised approach [R. Friedrich et al., Physics Letters A 271, 217…
In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…
This paper proposes an adaptive time-stepping mothods for stochastic diffusion systems whose drift and diffusion coefficients are locally Lipschitz continuous and may exhibit polynomial growth. By controlling the growth of both the drift…