Related papers: Estimating functions for jump-diffusions
The purpose of the present work is to construct estimators for the random effects in a fractional diffusion model using a hybrid estimation method where we combine parametric and nonparametric thechniques. We precisely consider $n$…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
The estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time-homogeneous case is classic, the time-inhomogeneous case has recently…
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the…
In this paper, we are presenting a method for estimation of market parameters modeled by jump diffusion process. The method proposed is based on Gibbs sampler, while the market parameters are the drift, the volatility, the jump intensity…
A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion…
We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…
We provide necessary and sufficient first order geometric conditions for the stochastic invariance of a closed subset of R^d with respect to a jump-diffusion under weak regularity assumptions on the coefficients. Our main result extends the…
Standard jump-diffusion models assume independence between jumps and diffusion components. We develop a multi-type jump-diffusion model where jump occurrence and magnitude depend on contemporaneous diffusion movements. Unlike previous…
This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…
We introduce a simple model of diffusive jump process where a fee is charged for each jump. The nonlinear cost function is such that slow jumps incur a flat fee, while for fast jumps the cost is proportional to the velocity of the jump. The…
Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…
We consider a jump-diffusion process on a bounded domain with reflection at the boundary, and establish long-term results for a general additive process of its path. This includes the long-term behaviour of its occupation time in the…
We study the problem of parameter estimation for large exchangeable interacting particle systems when a sample of discrete observations from a single particle is known. We propose a novel method based on martingale estimating functions…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
Asymptotic radiative transfer (ART), like diffusion theory, assumes the angular intensity distribution incident at a boundary is identical with that in the depth of the scattering medium. However, the asymptotic intensity profile and…
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…
Consider the sum $Y=B+B(H)$ of a Brownian motion $B$ and an independent fractional Brownian motion $B(H)$ with Hurst parameter $H\in(0,1)$. Even though $B(H)$ is not a semimartingale, it was shown in [\textit{Bernoulli} \textbf{7} (2001)…