Related papers: General alpha-Wiener bridges

Let us consider the process $(X_t^{(\alpha)})_{t\in[0,T)}$ given by the SDE $dX_t^{(\alpha)} = -\frac{\alpha}{T-t}X_t^{(\alpha)} dt+ dB_t$, $t\in[0,T)$, where $\alpha\in R$, $T\in(0,\infty)$, and $(B_t)_{t\geq 0}$ is a standard Wiener…

We collect, scattered through literature, as well as we prove some new properties of two Markov processes that in many ways resemble Wiener and Ornstein--Uhlenbeck processes. Although processes considered in this paper were defined either…

We study Karhunen-Loeve expansions of the process $(X_t^{(\alpha)})_{t\in[0,T)}$ given by the stochastic differential equation $dX_t^{(\alpha)} = -\frac\alpha{T-t} X_t^{(\alpha)} dt+ dB_t,$ $t\in[0,T),$ with an initial condition…

First we give a construction of bridges derived from a general Markov process using only its transition densities. We give sufficient conditions for their existence and uniqueness (in law). Then we prove that the law of the radial part of…

We derive bridges from general multidimensional linear non time-homogeneous processes using only the transition densities of the original process giving their integral representations (in terms of a standard Wiener process) and so-called…

This paper presents a study of the properties of the Ornstein-Uhlenbeck bridge, specifically, we derive its Karhunen-Lo\`eve expansion for any value of the initial variance and mean-reversion parameter (or mean-repulsion if negative). We…

We study sample path deviations of the Wiener process from three different representations of its bridge: anticipative version, integral representation and space-time transform. Although these representations of the Wiener bridge are equal…

In this paper, we study the Ornstein-Uhlenbeck bridge process (i.e. the Ornstein-Uhlenbeck process conditioned to start and end at fixed points) constraints to have a fixed area under its path. We present both anticipative (in this case, we…

We study the problem of stopping an $\alpha$-Brownian bridge as close as possible to its global maximum. This extends earlier results found for the Brownian bridge (the case $\alpha=1$). The exact behavior for $\alpha$ close to $0$ is…

We consider a one dimensional L\'evy bridge x_B of length n and index 0 < \alpha < 2, i.e. a L\'evy random walk constrained to start and end at the origin after n time steps, x_B(0) = x_B(n)=0. We compute the distribution P_B(A,n) of the…

A Markovian bridge is a probability measure taken from a disintegration of the law of an initial part of the path of a Markov process given its terminal value. As such, Markovian bridges admit a natural parameterization in terms of the…

In this paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein-Uhlenbeck process which is defined as the solution of $dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t$, and which is observed in…

We study the statistical inference problem for a complex $\alpha$-fractional Brownian bridge process $Z$ defined by the stochastic differential equation \[ \mathrm{d}Z_t = -\alpha \frac{Z_t}{T - t} \mathrm{d}t + \mathrm{d}\zeta_t, \quad t…

Schubert proved that, given a composite link $K$ with summands $K_{1}$ and $K_{2}$, the bridge number of $K$ satisfies the following equation: $$\beta(K)=\beta(K_{1})+\beta(K_{2})-1.$$ In ``Conway Produts and Links with Multiple Bridge…

We are interested in the law of the first passage time of an Ornstein-Uhlenbeck process to time-varying thresholds. We show that this problem is connected to the laws of the first passage time of the process to members of a two-parameter…

Let $U_n=[u_{i,j}]$ be the eigenvectors matrix of a Wigner matrix. We prove that under some moments conditions, the bivariate random process indexed by $[0,1]^2$ with value at $(s,t)$ equal to the sum, over $1\le i \le ns$ and $1\le j \le…

A generalized bridge is the law of a stochastic process that is conditioned on N linear functionals of its path. We consider two types of representations of such bridges: orthogonal and canonical. The orthogonal representation is…

For an arbitrary Hilbert space-valued Ornstein-Uhlenbeck process we construct the Ornstein-Uhlenbeck Bridge connecting a starting point $x$ and an endpoint $y$ that belongs to a certain linear subspace of full measure. We derive also a…

We prove an invariance principle for the bridge of a random walk conditioned to stay positive, when the random walk is in the domain of attraction of a stable law, both in the discrete and in the absolutely continuous setting. This includes…

We consider random walks X_n in Z+, obeying a detailed balance condition, with a weak drift towards the origin when X_n tends to infinity. We reconsider the equivalence in law between a random walk bridge and a 1+1 dimensional…