Related papers: Multiscale Jump Testing and Estimation Under Compl…
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
If we know that some kind of sequence always converges, we can ask how quickly and how uniformly it converges. Many convergent sequences converge non-uniformly and, relatedly, have no computable rate of convergence. However proof-theoretic…
This paper develops a robust parametric framework for jump detection in discretely observed CKLS-type jump-diffusion processes with high-frequency asymptotics, based on the minimum density power divergence estimator (MDPDE). The methodology…
Time estimation is a fundamental task that underpins precision measurement, global navigation systems, financial markets, and the organisation of everyday life. Many biological processes also depend on time estimation by nanoscale clocks,…
As a highly expressive generative model, diffusion models have demonstrated exceptional success across various domains, including image generation, natural language processing, and combinatorial optimization. However, as data distributions…
In this paper, we present the double smoothed nonparametric approach for infinitesimal conditional volatility of jump-diffusion model based on high frequency data. Under certain minimal conditions, we obtain the strong consistency and…
In this paper,we consider a macro approximation of the flow of a risk reserve, The process is observed at discrete time points. Because we cannot directly observe each jump time and size then we will make use of a technique for identifying…
This note extends some results of Nishiyama [Ann. Probab. 28 (2000) 685--712]. A maximal inequality for stochastic integrals with respect to integer-valued random measures which may have infinitely many jumps on compact time intervals is…
In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on $\mu$ and volatility coefficient depends on $\sigma$, two unknown parameters. We suppose that the process is discretely observed at the…
We evaluate the significance of a recently proposed bivariate jump-diffusion model for a data-driven characterization of interactions between complex dynamical systems. For various coupled and non-coupled jump-diffusion processes, we find…
The segmentation of data into stationary stretches also known as multiple change point problem is important for many applications in time series analysis as well as signal processing. Based on strong invariance principles, we analyse data…
We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data,…
A new approach to detect change points based on differential smoothing and multiple testing is presented for long data sequences modeled as piecewise constant functions plus stationary ergodic Gaussian noise. As an application of the STEM…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
In this paper, we study an optimal control problem of a mean-field forward-backward stochastic system with random jumps in progressive structure, where both regular and singular controls are considered in our formula. In virtue of the…
In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional…
This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise…
This paper deals with the problem of asymptotically optimal detection of changes in regime-switching stochastic models. We need to divide the whole obtained sample of data into several sub-samples with observations belonging to different…