Related papers: Clustering of discretely observed diffusion proces…
We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their generative models without prior knowledge of the model statistics and the number of generative models. Two…
The separating time for two probability measures on a filtered space is an extended stopping time which captures the phase transition between equivalence and singularity. More specifically, two probability measures are equivalent before…
In this paper, we aim to study the diffusion approximation for multi-scale McKean-Vlasov stochastic differential equations. More precisely, we prove the weak convergence of slow process $X^\varepsilon$ in $C([0,T];\mathbb{R}^n)$ towards the…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…
This paper develops new mathematical techniques to identify temporal shifts among a collection of US equities partitioned into a new and more detailed set of market sectors. Although conceptually related, our three analyses reveal distinct…
This paper proposes a novel similarity measure for clustering sequential data. We first construct a common state-space by training a single probabilistic model with all the sequences in order to get a unified representation for the dataset.…
A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Motivations for this scheme come typically…
We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of…
The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive…
This paper studies the sensitivity analysis of mass-action systems against their diffusion approximations, particularly the dependence on population sizes. As a continuous time Markov chain, a mass-action system can be described by a…
Uncertainty propagation in non-linear dynamical systems has become a key problem in various fields including control theory and machine learning. In this work we focus on discrete-time non-linear stochastic dynamical systems. We present a…
Diffusion processes have been widely used for approximations in the queueing theory. There are different types of diffusion approximations. Among them, we are interested in those obtained through limits of a sequence of models which…
In this work, we study a dynamic portfolio optimization problem related to pairs trading, which is an investment strategy that matches a long position in one security with a short position in another security with similar characteristics.…
An algorithm for determining stationary periods for time series of random sea waves is proposed in this work. This is a problem in which changes between stationary sea states are usually slow and segmentation procedures based on…
Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…
We analyse diffusion dynamics on weakly-coupled networks (interconnected networks) by means of separation of time scales. Using an adiabatic approximation we reduced the system dynamics to a Markov chain with aggregated variables and…
We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settings are analyzed: hidden…
Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
An unsupervised classification method for point events occurring on a network of lines is proposed. The idea relies on the distributional flexibility and practicality of random partition models to discover the clustering structure featuring…