Related papers: Maximum Likelihood Estimation of Diffusions by Con…
Information-theoretic quantities play a crucial role in understanding non-linear relationships between random variables and are widely used across scientific disciplines. However, estimating these quantities remains an open problem,…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
Discrete diffusion models (DDMs) are a powerful class of generative models for categorical data, but they typically require many function evaluations for a single sample, making inference expensive. Existing acceleration methods either rely…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
Piecewise deterministic Markov process samplers are attractive alternatives to Metropolis--Hastings algorithms. A central design question is how to incorporate partial velocity refreshment to ensure ergodicity without injecting excessive…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. A\"{\i}t-Sahalia [J. Finance 54 (1999)…
We present discrete-time approximation of optimal control policies for infinite horizon discounted/ergodic control problems for controlled diffusions in $\Rd$\,. In particular, our objective is to show near optimality of optimal policies…
We employ uncertain parametric CTMCs with parametric transition rates and a prior on the parameter values. The prior encodes uncertainty about the actual transition rates, while the parameters allow dependencies between transition rates.…
Identifying important features linked to a response variable is a fundamental task in various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a…
Finite state space hidden Markov models are flexible tools to model phenomena with complex time dependencies: any process distribution can be approximated by a hidden Markov model with enough hidden states.We consider the problem of…
We propose a method for obtaining maximum likelihood estimates (MLEs) of a Markov-Modulated Jump-Diffusion Model (MMJDM) when the data is a discrete time sample of the diffusion process, the jumps follow a Laplace distribution, and the…
Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest…
We study a new parametric approach for hidden discrete-time diffusion models. This method is based on contrast minimization and deconvolution and leads to estimate a large class of stochastic models with nonlinear drift and nonlinear…
We introduce Projected Latent Markov Chain Monte Carlo (PL-MCMC), a technique for sampling from the high-dimensional conditional distributions learned by a normalizing flow. We prove that a Metropolis-Hastings implementation of PL-MCMC…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
Bond rating Transition Probability Matrices (TPMs) are built over a one-year time-frame and for many practical purposes, like the assessment of risk in portfolios or the computation of banking Capital Requirements (e.g. the new IFRS 9…
Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved…
Diffusion processes are widely used for modelling real-world phenomena. Except for select cases however, analytical expressions do not exist for a diffusion process' transitional probabilities. It is proposed that the cumulant truncation…