Related papers: Intervention in Ornstein-Uhlenbeck SDEs
We consider a problem of parameter estimation for the state space model described by linear stochastic differential equations. We assume that an unobservable Ornstein-Uhlenbeck process drives another observable process by the linear…
By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…
In this paper, we study the Ornstein-Uhlenbeck bridge process (i.e. the Ornstein-Uhlenbeck process conditioned to start and end at fixed points) constraints to have a fixed area under its path. We present both anticipative (in this case, we…
We propose a physical analogy between finding the solution of an ordinary differential equation (ODE) and a $N$ particle problem in statistical mechanics. It uses the fact that the solution of an ODE is equivalent to obtain the minimum of a…
In this paper we study the linear and nonlinear Schr\"odinger equations associated with the Ornstein-Uhlenbeck (OU) operator endowed with the Gaussian measure. While classical Strichartz estimates are well-developed for the free…
Computing the stochastic entropy production associated with the evolution of a stochastic dynamical system is a well-established problem. In a small number of cases such as the Ornstein-Uhlenbeck process, of which we give a complete…
Causal inference methods are widely applied in various decision-making domains such as precision medicine, optimal policy and economics. Central to these applications is the treatment effect estimation of intervention strategies. Current…
The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It…
We consider a non-linear parabolic partial differential equation (PDE) on $\mathbb R^d$ with a distributional coefficient in the non-linear term. The distribution is an element of a Besov space with negative regularity and the non-linearity…
The existence of stationary distributions to distribution dependent stochastic differential equations are investigated by using the ergodicity of the associated decoupled equation and the Schauder fixed point theorem. By using Zvonkin's…
Causal inference methods are widely applied in various decision-making domains such as precision medicine, optimal policy and economics. Central to causal inference is the treatment effect estimation of intervention strategies, such as…
This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects. The Lie…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…
In this paper backward stochastic differential equations with interaction (shorter BSDEs with interaction) are introduced. Far to our knowledge, this type of equation is not seen in the literature before. Existence and uniqueness result for…
We investigate the dynamics of an inertial active Ornstein-Uhlenbeck (OU) particle in the presence of stochastic resetting. Using renewal approach, we compute the mean square displacement (MSD) and position probability distribution…
We further elaborate on the solvability of stochastic partial differential equations (SPDEs). We shall discuss non-autonomous partial differential equations with an abstract realization of the stochastic integral on the right-hand side. Our…
This article studies the effect of discretisation error on the stationary distribution of stochastic partial differential equations (SPDEs). We restrict the analysis to the effect of space discretisation, performed by finite element…
We consider a linear stochastic differential equation with stochastic drift. We study the problem of approximating the solution of such equation through an Ornstein-Uhlenbeck type process, by using direct methods of calculus of variations.…
We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete observations of such dynamics in stationary…
In this paper, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the $Y$-component of the solution enters in both the driver…