Related papers: Characteristics of the switch process and geometri…
Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We…
In this research article, we consider the uniqueness sequences for multidimensional vector-valued Laplace transform. We establish the fundamental relationships between uniqueness sequences for one-dimensional Laplace transform and…
Markov switching models are a popular family of models that introduces time-variation in the parameters in the form of their state- or regime-specific values. Importantly, this time-variation is governed by a discrete-valued latent…
We compute the transition probability between two learning tasks, and show that it decomposes into two factors. The first depends on the geometry of the loss landscape of a model trained on each task, independent of any particular model…
We discuss a single-server multi-station alternating queue where the preparation times and the service times are auto- and cross-correlated. We examine two cases. In the first case, preparation and service times depend on a common discrete…
This paper considers differential problems with random switching, with specific applications to the motion of cells and centrally coordinated motion. Starting with a differential-equation model of cell motion that was proposed previously,…
We investigate the one-dimensional telegraph random process in the presence of an elastic boundary at the origin. This process describes a finite-velocity random motion that alternates between two possible directions of motion (positive or…
For a given wave function one can define a quantity $\mu_E$ having a meaning of its inverse spatial size. The Laplace transform of the distribution function $P(\mu_E)$ is calculated analytically for a 1D disordered sample with a finite…
In this short note the theory for multivariate asset allocation with elliptically symmetric distributions of returns, as developed in the author's prior work, is specialized to the case of returns drawn from a multivariate Laplace…
If a system is at thermodynamic equilibrium, an observer cannot tell whether a film of it is being played forward or in reverse: any transition will occur with the same frequency in the forward as in the reverse direction. However, if…
In this article we determine the Laplace transforms of the main boundary functionals of the oscillating compound Poisson process. These are the first passage time of the level, the joint distribution of the first exit time from the interval…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
A novel switching differentiator that has considerably simple form is proposed. Under the assumption that time-derivatives of the signal are norm-bounded, it is shown that estimation errors are convergent to the zeros asymptotically. The…
The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of…
Resetting a stochastic process is an important problem describing the evolution of physical, biological and other systems which are continually returned to their certain fixed point. We consider the motion of a subdiffusive particle with a…
We characterize the class of exchangeable Feller processes evolving on partitions with boundedly many blocks. In continuous-time, the jump measure decomposes into two parts: a $\sigma$-finite measure on stochastic matrices and a collection…
We study the problem of estimating the value function of discrete-time switched systems under arbitrary switching. Unlike the switched LQR problem, where both inputs and mode sequences are optimized, we consider the case where switching is…
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant…
We discuss the conditions under which identical particles may yet be distinguishable and the relationship between particle permutation and exchange. We show that we can always define permutation-symmetric state vectors. When the particles…
We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…