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This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
Many causal estimands are only partially identifiable since they depend on the unobservable joint distribution between potential outcomes. Stratification on pretreatment covariates can yield sharper bounds; however, unless the covariates…
In this paper, enlightened by the asymptotic expansion methodology developed by Li(2013b) and Li and Chen (2016), we propose a Taylor-type approximation for the transition densities of the stochastic differential equations (SDEs) driven by…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…
We present a method for the nonparametric estimation of the drift function of certain types of stochastic differential equations from the empirical density. It is based on a variational formulation of the Fokker-Planck equation. The…
In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…
In the pathwise stochastic calculus framework, the paper deals with the general study of equations driven by an additive Gaussian noise, with a drift function having an infinite limit at point zero. An ergodic theorem and the convergence of…
We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown flow map of the underlying system. It employs the idea of…
This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric $\alpha$-stable L\'{e}vy motion ($0<\alpha<1$) or Brownian motion. For stochastic dynamical systems…
We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of…
The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven…
We develop a new approach for estimating the risk of an arbitrary estimator of the mean vector in the classical normal means problem. The key idea is to generate two auxiliary data vectors, by adding carefully constructed normal noise…
Levy processes are widely used in financial mathematics, telecommunication, economics, queueing theory and natural sciences for modelling. A typical model is obtained by considering finite dimensional linear stochastic SISO systems driven…
In supervised learning, the estimation of prediction error on unlabeled test data is an important task. Existing methods are usually built on the assumption that the training and test data are sampled from the same distribution, which is…
We propose an unbiased Monte-Carlo estimator for $\mathbb{E}[g(X_{t_1}, \cdots, X_{t_n})]$, where $X$ is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a…
We propose an open loop methodology based on sample statistics to solve chance constrained stochastic optimal control problems with probabilistic safety guarantees for linear systems where the additive Gaussian noise has unknown mean and…
Monitoring machine learning models once they are deployed is challenging. It is even more challenging to decide when to retrain models in real-case scenarios when labeled data is beyond reach, and monitoring performance metrics becomes…
We consider the development of unbiased estimators, to approximate the stationary distribution of Mckean-Vlasov stochastic differential equations (MVSDEs). These are an important class of processes, which frequently appear in applications…
This paper focuses on a stochastic system identification problem: given time series observations of a stochastic differential equation (SDE) driven by L\'{e}vy $\alpha$-stable noise, estimate the SDE's drift field. For $\alpha$ in the…