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We consider a class of sequential decision-making problems under uncertainty that can encompass various types of supervised learning concepts. These problems have a completely observed state process and a partially observed modulation…
In this article we explore the phenomena of nonequilibrium stochastic process starting from the phenomenological Brownian motion. The essential points are described in terms of Einstein's theory of Brownian motion and then the theory…
We consider two dependent Brownian motions with (possibly) different drift, and apply a result by le Gall on cone points of two dimensional Brownian motion to show that with probability one, there will not be a time that is a local maximum…
We consider Langevin equation involving fractional Brownian motion with Hurst index $H\in(0,\frac12)$. Its solution is the fractional Ornstein-Uhlenbeck process and with unknown drift parameter $\theta$. We construct the estimator that is…
We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an on-off input process. We study stochastic control problems associated with the long-run…
We calculate the large deviation functions characterizing the long-time fluctuations of the occupation of drifted Brownian motion and show that these functions have non-analytic points. This provides the first example of dynamical phase…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
The purpose of this paper is to review and highlight some connections between the problem of nonlinear smoothing and optimal control of the Liouville equation. The latter has been an active area of recent research interest owing to work in…
$N$-Brownian bees is a branching-selection particle system in $\mathbb{R}^d$ in which $N$ particles behave as independent binary branching Brownian motions, and where at each branching event, we remove the particle furthest from the origin.…
In this paper, we are concerned with a stochastic optimal control problem of mean-field type under partial observation, where the state equation is governed by the controlled nonlinear mean-field stochastic differential equation, moreover…
Inverse optimal control can be used to characterize behavior in sequential decision-making tasks. Most existing work, however, is limited to fully observable or linear systems, or requires the action signals to be known. Here, we introduce…
We study a class of mean-field control problems under partial observation. The controlled dynamics are of McKean-Vlasov type and are subject to regime switching driven by a hidden Markov chain. The observation process depends on the control…
Suppose that $(X_t)_{t \ge 0}$ is a one-dimensional Brownian motion with negative drift $-\mu$. It is possible to make sense of conditioning this process to be in the state $0$ at an independent exponential random time and if we kill the…
We consider the problem of stabilizing the coherence of a single qubit subject to Markovian decoherence, via the application of a control Hamiltonian, without any additional resources. In this case neither quantum error…
Let $B = (B_t)_{t \in {\bf R}}$ be a symmetric Brownian motion, i.e. $(B_t)_{t \in {\bf R}_+}$ and $(B_{-t})_{t \in {\bf R}_+}$ are independent Brownian motions starting at $0$. Given $a \ge b>0$, we describe the law of the random set…
We consider the problem of reconstructing the cross--power spectrum of an unobservable multivariate stochatic process from indirect measurements of a second multivariate stochastic process, related to the first one through a linear…
We study a finite-horizon covariance steering problem for discrete-time Markov jump linear systems (MJLS) with both state- and control-dependent multiplicative noise. The objective is to minimize a quadratic running cost while steering the…
In this article we consider a Brownian motion with drift of the form \[dS_t=\mu_t dt+dB_t\qquadfor t\ge0,\] with a specific nontrivial $(\mu_t)_{t\geq0}$, predictable with respect to $\mathbb{F}^B$, the natural filtration of the Brownian…
A stochastic leap-frog algorithm for the numerical integration of Brownian motion stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time…
Motivated by the Internet-of-things and sensor networks for cyberphysical systems, the problem of dynamic sensor activation for the tracking of a time-varying process is examined. The tradeoff is between energy efficiency, which decreases…