Related papers: The Minimax Wiener Sequential Testing Problem
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…
We study Bayes procedures for the problem of nonparametric drift estimation for one-dimensional, ergodic diffusion models from discrete-time, low-frequency data. We give conditions for posterior consistency and verify these conditions for…
This paper considers a version of the Wiener filtering problem for equalization of passive quantum linear quantum systems. We demonstrate that taking into consideration the quantum nature of the signals involved leads to features typically…
Sequential change diagnosis is the joint problem of detection and identification of a sudden and unobservable change in the distribution of a random sequence. In this problem, the common probability law of a sequence of i.i.d. random…
We study the weak error associated with the Euler scheme of non degenerate diffusion processes with non smooth bounded coefficients. Namely, we consider the cases of H{\"o}lder continuous coefficients as well as piecewise smooth drifts with…
Jump diffusion processes are widely used to model asset prices over time, mainly for their ability to capture complex discontinuous behavior, but inference on the model parameters remains a challenge. Here our goal is posterior inference on…
The input-output behaviour of the Wiener neuronal model subject to alternating input is studied under the assumption that the effect of such an input is to make the drift itself of an alternating type. Firing densities and related…
The problem of determining a periodic Lipschitz vector field $b=(b_1, \dots, b_d)$ from an observed trajectory of the solution $(X_t: 0 \le t \le T)$ of the multi-dimensional stochastic differential equation \begin{equation*} dX_t =…
In the quickest change detection problem in which both nuisance and critical changes may occur, the objective is to detect the critical change as quickly as possible without raising an alarm when either there is no change or a nuisance…
We establish an averaging principle for a structural multiscale stochastic nonlinear fractional Schr\"odinger system on the one-dimensional torus driven by a multiplicative Wiener noise. The slow component is governed by a fractional…
We consider a linear stochastic differential equation with stochastic drift and multiplicative noise. We study the problem of approximating its solution with the process that solves the equation where the possibly stochastic drift is…
We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…
In this paper, we study a discrete-time stochastic optimal control problem under distribution uncertainty with convex control domain. By weak convergence method and Sion's minimax theorem, we obtain the variational inequality for cost…
We consider a controlled second order differential equation which is partially observed with an additional fractional noise. we study the asymptotic (for large observation time) design problem of the input and give an efficient estimator of…
We consider nonparametric Bayesian inference in a reflected diffusion model $dX_t = b (X_t)dt + \sigma(X_t) dW_t,$ with discretely sampled observations $X_0, X_\Delta, \dots, X_{n\Delta}$. We analyse the nonlinear inverse problem…
For an arbitrary diffusion process $X$ with time-homogeneous drift and variance parameters $\mu(x)$ and $\sigma^2(x)$, let $V_\varepsilon$ be $1/\varepsilon$ times the total time $X(t)$ spends in the strip…
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…
Sensors based on single spins can enable magnetic field detection with very high sensitivity and spatial resolution. Previous work has concentrated on sensing of a constant magnetic field or a periodic signal. Here, we instead investigate…