相关论文: Bias-correction of the maximum likelihood estimato…

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…

An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on…

We study a simple decision problem on the scaling parameter in the $\alpha$-Brownian bridge $X^{(\alpha)}$ on the interval $[0,1]$: given two values $\alpha_0, \alpha_1 \geq 0$ with $\alpha_0 + \alpha_1 \geq 1$ and some time $0 \leq T \leq…

Let alpha,T>0. We study the asymptotic properties of a least squares estimator for the parameter alpha of a fractional bridge defined as dX_t=-alpha*X_t/(T-t)dt+dB_t, with t in [0,T) and where B is a fractional Brownian motion of Hurst…

Let $T>0,\alpha>\frac12$. In the present paper we consider the $\alpha$-Brownian bridge defined as $dX_t=-\alpha\frac{X_t}{T-t}dt+dW_t,~ 0\leq t< T$, where $W$ is a standard Brownian motion. We investigate the optimal rate of convergence to…

Fractional Brownian motion is a self-affine, non-Markovian and translationally invariant generalization of Brownian motion, depending on the Hurst exponent $H$. Here we investigate fractional Brownian motion where both the starting and the…

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…

The problem of stopping a Brownian bridge with an unknown pinning point to maximise the expected value at the stopping time is studied. A few general properties, such as continuity and various bounds of the value function, are established.…

We study the law of the minimum of a Brownian bridge, conditioned to take specific values at specific points, and the law of the location of the minimum. They are used to compare some non-adaptive optimisation algorithms for black-box…

We consider the problem of optimally stopping a Brownian bridge with an unknown pinning time so as to maximise the value of the process upon stopping. Adopting a Bayesian approach, we assume the stopper has a general continuous prior and is…

We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved…

In this paper, we introduce an extension of a Brownian bridge with a random length by including uncertainty also in the pinning level of the bridge. The main result of this work is that unlike for deterministic pinning point, the bridge…

The conditional density of Brownian motion is considered given the max, B(t|\max), as well as those with additional information: B(t|close, max), B(t|close, max, min) and B(t|max, min) where the close is the final value: B(t=1)=c and t in…

We consider non-colliding Brownian bridges starting from two points and returning to the same position. These positions are chosen such that, in the limit of large number of bridges, the two families of bridges just touch each other forming…

We consider the problem of constructing an adaptive bridge regression modeling, which is a penalized procedure by imposing different weights to different coefficients in the bridge penalty term. A crucial issue in the modeling process is…

Consider the {$\ell_{\alpha}$} regularized linear regression, also termed Bridge regression. For $\alpha\in (0,1)$, Bridge regression enjoys several statistical properties of interest such as sparsity and near-unbiasedness of the estimates…

Binary classifiers trained on a certain proportion of positive items introduce a bias when applied to data sets with different proportions of positive items. Most solutions for dealing with this issue assume that some information on the…

We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditioned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge…

We introduce a resetting Brownian bridge as a simple model to study search processes where the total search time $t_f$ is finite and the searcher returns to its starting point at $t_f$. This is simply a Brownian motion with a Poissonian…

Motivated by evaluating the limiting distribution of randomly biased random walks on trees, we compute the exact value of a negative moment of the maximal drawdown of the standard Brownian meander.