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We consider a control constrained parabolic optimal control problem and use variational discretization for its time semi-discretization. The state equation is treated with a Petrov-Galerkin scheme using a piecewise constant Ansatz for the…
We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…
This paper focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…
We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…
This paper considers the temporal discretization of an inverse problem subject to a time fractional diffusion equation. Firstly, the convergence of the L1 scheme is established with an arbitrary sectorial operator of spectral angle $< \pi/2…
Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…
This paper is concerned with the partial information optimal control problem of wa controlled forward-backward stochastic differential equation of jump diffusion with correlated noises between the system and the observation. For this type…
Adapting pretrained diffusion models to downstream objectives such as inverse problems often requires expensive test-time guidance or optimization. We propose a principled framework for generating high-quality reward-aligned samples at…
While imitation learning provides a simple and effective framework for policy learning, acquiring consistent actions during robot execution remains a challenging task. Existing approaches primarily focus on either modifying the action…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the discontinuity in the initial condition and also satisfies the…
This work collects some methodological insights for numerical solution of a "minimum-dispersion" control problem for nonlinear stochastic differential equations, a particular relaxation of the covariance steering task. The main ingredient…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity,…
The application of deep learning for partial differential equation (PDE)-constrained control is gaining increasing attention. However, existing methods rarely consider safety requirements crucial in real-world applications. To address this…
We give a probabilistic interpretation of the Monte Carlo scheme proposed by Fahim, Touzi and Warin [Ann. Appl. Probab. 21 (2011) 1322-1364] for fully nonlinear parabolic PDEs, and hence generalize it to the path-dependent (or…
We analyze an optimal control problem with pointwise tracking for a fractional semilinear elliptic partial differential equation. The diffusion is characterized by the spectral fractional Laplacian $(-\Delta)^s$ with $s \in (1/2,1)$, a…
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
We study the estimation of the value function for continuous-time Markov diffusion processes using a single, discretely observed ergodic trajectory. Our work provides non-asymptotic statistical guarantees for the least-squares…