Related papers: Quickest drift change detection in L\'evy-type for…
The problem of quickest change detection is studied, where there is an additional constraint on the cost of observations used before the change point and where the post-change distribution is composite. Minimax formulations are proposed for…
This paper studies a general L\'evy process model of the bail-out optimal dividend problem with an exponential time horizon, and further extends it to the regime-switching model. We first show the optimality of a double barrier strategy in…
Consider the motion of a Brownian particle in $n$ dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, exactly $k$ of the coordinate processes get a…
L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…
In this paper, we focus on the statistical filtering problem in dynamical models with jumps. When a particular application relies on physical properties which are modeled by linear and Gaussian probability density functions with jumps, an…
A random sequence having two segments being the homogeneous Markov processes is registered. Each segment has his own transition probability law and the length of the segment is unknown and random. The transition probabilities of each…
With today's abundant streams of data, the only constant we can rely on is change. For stream classification algorithms, it is necessary to adapt to concept drift. This can be achieved by monitoring the model error, and triggering counter…
This paper introduces an approach to multi-stream quickest change detection and fault isolation for unnormalized and score-based statistical models. Traditional optimal algorithms in the quickest change detection literature require explicit…
In this paper we present new theoretical results on optimal estimation of certain random quantities based on high frequency observations of a L\'evy process. More specifically, we investigate the asymptotic theory for the conditional mean…
The {\alpha}-stable L\'evy process, commonly used to describe L\'evy flight, is characterized by discontinuous jumps and is widely used to model anomalous transport phenomena. In this study, we investigate the associated exit problem and…
We consider a fractional Brownian motion with unknown linear drift such that the drift coefficient has a prior normal distribution and construct a sequential test for the hypothesis that the drift is positive versus the alternative that it…
We study a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift. The drift coefficient is assumed to decompose as $b(t,x,a)=b_1(t,x)+b_2(x)b_3(t,a)$, where $b_1$ is bounded and…
This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…
The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast…
The quickest change detection problem is considered in the context of monitoring large-scale independent normal distributed data streams with possible changes in some of the means. It is assumed that for each individual local data stream,…
Common statistical prediction models often require and assume stationarity in the data. However, in many practical applications, changes in the relationship of the response and predictor variables are regularly observed over time, resulting…
This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The…
A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte…
We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…