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The analysis of local minima in time series data and random landscapes is essential across numerous scientific disciplines, offering critical insights into system dynamics. Recently, Kundu, Majumdar, and Schehr derived the exact…
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Let $B^{a,b}:=\{B_t^{a,b},t\geq0\}$ be a weighted fractional Brownian motion of parameters $a>-1$, $|b|<1$, $|b|<a+1$. We consider a least square-type method to estimate the drift parameter $\theta>0$ of the weighted fractional…
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Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
We consider a system of noncolliding Brownian motions introduced in our previous paper, in which the noncolliding condition is imposed in a finite time interval $(0,T]$. This is a temporally inhomogeneous diffusion process whose transition…
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Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an…
In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below by a strictly positive constant uniformly in time. Allowing…
Using the determinantal formula of Biane, Bougerol, and O'Connell, we give multitime joint probability densities to the noncolliding Brownian motion with drift, where the number of particles is finite. We study a special case such that the…