相关论文: Weak existence of the squared Bessel process and C…

We study strong (pathwise) approximation of Cox-Ingersoll-Ross processes. We propose a Milstein-type scheme that is suitably truncated close to zero, where the diffusion coefficient fails to be locally Lipschitz continuous. For this scheme…

We study the sticky Cox-Ingersoll-Ross (CIR) process in one dimension, a diffusion on $[0,\infty)$ with a sticky boundary condition at the origin, arising as the marginal process in a sparse Bayesian inference framework based on…

We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…

Complex dynamical systems are prevalent in many scientific disciplines. In the analysis of such systems two aspects are of particular interest: 1) the temporal patterns along which they evolve and 2) the underlying causal mechanisms.…

We introduce a fractional Bessel process with constant negative drift, defined as a time-changed Bessel process via the inverse of a stable subordinator, independent of the base process. This construction yields a model capable of capturing…

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…

Inverse initial and inverse source problems of a time-fractional differential equation with Bessel operator are considered. Results on existence and uniqueness of solutions to these problems are presented. The solution method is based on…

In car-following models, the driver reacts according to his physical and psychological abilities which may change over time. However, most car-following models are deterministic and do not capture the stochastic nature of human perception.…

We determine the processes obtained from a large class of reflected Brownian motions (RBMs) in the nonnegative orthant by means of time reversal. The class of RBMs we deal with includes, but is not limited to, RBMs in the so-called…

We present simple assumptions on the constraints defining a hard core dynamics for the associated reflected stochastic differential equation to have a unique strong solution. Time-reversibility is proven for gradient systems with normal…

In this paper the Feynman Green function for Maxwell's theory in curved space-time is studied by using the Fock-Schwinger-DeWitt asymptotic expansion; the point-splitting method is then applied, since it is a valuable tool for regularizing…

We prove the unique weak solvability of time-inhomogeneous stochastic differential equations with additive noises and drifts in critical Lebsgue space $L^q([0,T]; L^{p}(\mathbb{R}^d))$ with $d/p+2/q=1$. The weak uniqueness is obtained by…

We consider a two dimensional reflecting random walk on the nonnegative integer quadrant. It is assumed that this reflecting random walk has skip free transitions. We are concerned with its time reversed process assuming that the stationary…

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…

We study adaptive sensing of Cox point processes, a widely used model from spatial statistics. We introduce three tasks: maximization of captured events, search for the maximum of the intensity function and learning level sets of the…

We derive differential equations for multiplicative statistics of the Bessel determinantal point process depending on two parameters. In particular, we prove that such statistics are solutions to an integrable nonlinear partial differential…

We propose a class of tests for linear regression on concomitants (induced order statistics). These tests are based on sequential sums of regression residuals. We self-center and self-normalize these sums. The resulting process is called an…

Dynamical low-rank approximation in the Tucker tensor format of given large time-dependent tensors and of tensor differential equations is the subject of this paper. In particular, a discrete time integration method for rank-constrained…

The log Gaussian Cox process is a flexible class of Cox processes, whose intensity surface is stochastic, for incorporating complex spatial and time structure of point patterns. The straightforward inference based on Markov chain Monte…

Passive discrete-time systems with Hilbert spaces as an incoming and outgoing space and a Pontryagin space as a state space are investigated. A geometric characterization when the index of the transfer function coincides with the negative…