Related papers: Representations of multidimensional linear process…
In this paper we introduce the well-balanced L\'{e}vy driven Ornstein-Uhlenbeck process as a moving average process of the form $X_t=\int \exp(-\lambda |t-u|)dL_u$. In contrast to L\'{e}vy driven Ornstein-Uhlenbeck processes the…
We consider the generalized Ornstein- Uhlenbeck equation $\partial_t X=-m X_t+\eta$. In this paper We construct the L\'evy noise $\eta$. The generalized Ornstein- Uhlenbeck process $X_t$ will be represented by a special types of graphs…
Quadratic harnesses are typically non-homogeneous Markov processes with time-dependent state space. Using an appropriately defined affine transformation we show that all bridges of a given quadratic harness can be transformed into other…
Many physical and biological systems rely on the progression of material through multiple independent stages. In viral replication, for example, virions enter a cell to undergo a complex process comprising several disparate stages before…
We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be…
Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we…
Modality translation is inherently under-constrained, as multiple cross-modal mappings may yield the same marginals. Recent work has shown that diffusion bridges are effective for this task. However, most existing approaches rely on fully…
This paper studies one-dimensional Ornstein-Uhlenbeck processes, with the distinguishing feature that they are reflected on a single boundary (put at level 0) or two boundaries (put at levels 0 and d>0). In the literature they are referred…
The survival probability and the first-passage-time statistics are important quantities in different fields. The Wiener process is the simplest stochastic processwith continuous variables, and important results can be explicitly found from…
We revisit classic ergodic large-deviation principles: for the occupation measure (Donsker-Varadhan), and for the empirical flux. We show that these problems can be embedded into a more general, discrete-time framework. A conditioning and…
We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on…
We consider the Schr\"odinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely"…
We derive the path-integral representation of the fractional Ornstein-Uhlenbeck process driven by Riemann-Liouville fractional Gaussian noise, for both the subdiffusive and superdiffusive regimes. We express the corresponding action, which…
We present evidence for a conjectural relationship between absorption times for discrete Whittaker processes and maximal heights of non-intersecting Brownian bridges.
In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first…
Ordinary Differential Equations are derived for the adjoint Euler equations firstly using the method of characteristics in 2D. For this system of partial-differential equations, the characteristic curves appear to be the streamtraces and…
I introduce a general, Bayesian method for modelling univariate time series data assumed to be drawn from a continuous, stochastic process. The method accommodates arbitrary temporal sampling, and takes into account measurement…
Score-based generative models exhibit state of the art performance on density estimation and generative modeling tasks. These models typically assume that the data geometry is flat, yet recent extensions have been developed to synthesize…
We study a version of the Ornstein-Uhlenbeck bridge driven by a spectrally-positive subordinator. Our formulation is based on a Linear-Quadratic control subject to a singular terminal condition. The Ornstein-Uhlenbeck bridge, we develop, is…
The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It…