相关论文: Weak backward error analysis for Langevin process
With this contribution, we shed light on the relation between the discrete adjoints of multistep backward differentiation formula (BDF) methods and the solution of the adjoint differential equation. To this end, we develop a…
This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…
Many scientific and engineering applications are formulated as inverse problems associated with stochastic models. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their…
We consider the numerical treatment of one of the most popular finite strain models of the viscoelastic Maxwell body. This model is based on the multiplicative decomposition of the deformation gradient, combined with Neo-Hookean…
For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first…
We prove a weak converse estimate for the simultaneous approximation by several forms of the Bernstein polynomials with integer coefficients. It is stated in terms of moduli of smoothness. In particular, it yields a big $O$-characterization…
In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK model. In order to avoid time step restrictions coming from convection term and small Knudsen number, we combine a semi-Lagrangian approach for the…
The limits of scaled relative entropies between probability distributions associated with N-particle weakly interacting Markov processes are considered. The convergence of such scaled relative entropies is established in various settings.…
We develop a framework for the compression of reversible Markov chains with rigorous error control. Given a subset of selected states, we construct reduced dynamics that can be lifted to an approximation of the full dynamics, and we prove…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
We prove that the inverse of a positive-definite matrix can be approximated by a weighted-sum of a small number of matrix exponentials. Combining this with a previous result [OSV12], we establish an equivalence between matrix inversion and…
In this contribution we are concerned with tight a posteriori error estimation for projection based model order reduction of $\inf$-$\sup$ stable parameterized variational problems. In particular, we consider the Reduced Basis Method in a…
We propose the difference weak measurement scheme, and illustrate its advantages for measuring small longitude phase-shift in high precision. Compared to the standard interferometry and standard weak measurement schemes, the proposed scheme…
In this paper, we introduce a method of converting implicit equations to the usual forms of functions locally without differentiability. For a system of implicit equations which are equipped with continuous functions, if there are unique…
This work is devoted to convergence analysis of an exponential integrator scheme for semi-discretization in time of nonlinear stochastic wave equation. A unified framework is first set forth, which covers important cases of additive and…
Although for a number of semilinear stochastic wave equations existence and uniqueness results for corresponding solution processes are known from the literature, these solution processes are typically not explicitly known and numerical…
We consider nonparametric estimation for functional autoregressive processes with Markov switching. First, we study the case where complete data is available; i.e. when we observe the Markov switching regime. Then we estimate the regression…
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…
We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter…
Stochastic kinetic models describe systems across biology, chemistry, and physics where discrete events and small populations render deterministic approximations inadequate. Parameter inference and inverse design in these systems require…