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We adapt the improved duality estimates for bounded coefficients derived by Canizo et al. to the framework of cross diffusion. Since the estimates can not be directly applied we need to derive a time discrete version of their results and…
In an ensemble of non-interacting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
This paper is concerned with combined inference for point processes on the real line observed in a broken interval. For such processes, the classic history-based approach cannot be used. Instead, we adapt tools from sequential spatial point…
In this paper, we consider the structural change in a class of discrete valued time series, which the true conditional distribution of the observations is assumed to be unknown. The conditional mean of the process depends on a parameter…
The one-dimensional Brownian motion starting from the origin at time $t=0$, conditioned to return to the origin at time $t=1$ and to stay positive during time interval $0 < t < 1$, is called the Bessel bridge with duration 1. We consider…
We consider the problem of Bayesian inference for bi-variate data observed in time but with observation times which occur non-synchronously. In particular, this occurs in a wide variety of applications in finance, such as high-frequency…
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…
In this paper, we focus on multiple sampling problems for the estimation of the fractional Brownian motion when the maximum number of samples is limited, extending existing results in the literature in a non-Markovian framework. Two classes…
Statistical techniques play a large role in the structural health monitoring of instrumented infrastructure, such as a railway bridge constructed with an integrated network of fibre optic sensors. One possible way to reason about the…
We study a linear filtering problem where the signal and observation processes are described as solutions of linear stochastic differential equations driven by time-space Brownian sheets. We derive a stochastic integral equation for the…
We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a non-trivial likelihood given the latent path. Due to the non-Markovianity and high-dimensionality of the latent paths,…
The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion bridges for modeling…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
We show in detail some results, outlined in a previous paper regarding the case of Brownian motion (BM), about the distribution of the $n$th-passage time of a one-dimensional diffusion obtained by a space or time transformation of BM,…
The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer…
Consider N Brownian bridges B_i:[-N,N] -> R, B_i(-N) = B_i(N) = 0, 1 <= i <= N, conditioned not to intersect. The edge-scaling limit of this system is obtained by taking a limit as N -> infinity of these curves scaled around (0,2^{1/2} N)…
In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of…
The time-dependent barrier passage of an anomalous system-reservoir coupling non-equilibrium open environment is studied where the heat bath is modulated by an external noise. The time-dependent barrier passing probability is obtained…
We consider $N$ non-intersecting Brownian bridges conditioned to stay below a fixed threshold. We consider a scaling limit where the limit shape is tangential to the threshold. In the large $N$ limit, we determine the limiting distribution…