Publications (20)
Fokker--Planck and Kolmogorov Backward Equations for Continuous Time Random Walk scaling limits
Boris Baeumer, Peter Straka
It is proved that the distributions of scaling limits of Continuous Time Random Walks (CTRWs) solve integro-differential equations akin to Fokker-Planck Equations for diffusion pro…
Incorporating the influence of sub-grid heterogeneity in regional-scale contaminant transport models
Boris Baeumer, Yong Zhang, Rina Schumer
Numerical transport models based on the advection-dispersion equation (ADE) are built on the assumption that sub-grid cell transport is Fickian such that dispersive spreading aroun…
Predicting the Drug Release Kinetics of Matrix Tablets
Boris Baeumer, Lipika Chatterjee, Peter Hinow +3
In this paper we develop two mathematical models to predict the release kinetics of a water soluble drug from a polymer/excipient matrix tablet. The first of our models consists of…
Reflected Spectrally Negative Stable Processes and their Governing Equations
Boris Baeumer, Mihály Kovács, Mark M. Meerschaert +2
This paper explicitly computes the transition densities of a spectrally negative stable process with index greater than one, reflected at its infimum. First we derive the forward e…
Boundary Conditions for Fractional Diffusion
Boris Baeumer, Mihály Kovács, Mark M. Meerschaert +1
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical p…
A Multidimensional Fractional Hawkes Process for Multiple Earthquake Mainshock Aftershock Sequences
Louis Davis, Boris Baeumer, Ting Wang
Most point process models for earthquakes currently in the literature assume the magnitude distribution is i.i.d. potentially hindering the ability of the model to describe the mai…
Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise
Boris Baeumer, Matthias Geissert, Mihaly Kovacs
We consider a class of semilinear Volterra type stochastic evolution equation driven by multiplicative Gaussian noise. The memory kernel, not necessarily analytic, is such that the…
Boundary conditions for nonlocal one-sided pseudo-differential operators and the associated stochastic processes II
Boris Baeumer, Mihály Kovács, Lorenzo Toniazzi
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided Lévy processes. On one hand this allows modellers to use appro…
Orientation in Poisson Cluster Processes via Imaginary Bispectra
Conor Kresin, Yifu Tang, Boris Baeumer +1
We study what remains detectable about one-sided Poisson cluster processes after cluster orientation is erased. We construct matched reversible cluster nulls preserving intensity a…
Boundary conditions for nonlocal one-sided pseudo-differential operators and the associated stochastic processes I
Boris Baeumer, Mihály Kovács, Lorenzo Toniazzi
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided Lévy processes. On one hand this allows modellers to use appro…
Space-time fractional Dirichlet problems
Boris Baeumer, Tomasz Luks, Mark M. Meerschaert
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an…
Higher order Grünwald approximations of fractional derivatives and fractional powers of operators
Boris Baeumer, Mihály Kovács, Harish Sankaranarayanan
We give stability and consistency results for higher order Grünwald-type formulae used in the approximation of solutions to fractional-in-space partial differential equations. We…
Fractional Partial Differential Equations with Boundary Conditions
Boris Baeumer, Mihály Kovács, Harish Sankaranarayanan
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for…
Space-time duality for fractional diffusion
Boris Baeumer, Mark M. Meerschaert, Erkan Nane
Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional…
Brownian subordinators and fractional Cauchy problems
Boris Baeumer, Mark M. Meerschaert, Erkan Nane
A Brownian time process is a Markov process subordinated to the absolute value of an independent one-dimensional Brownian motion. Its transition densities solve an initial value pr…
Spectral analysis of multivariate stationary Hawkes processes
Yifu Tang, Conor Kresin, Boris Baeumer +1
We establish the asymptotic validity of frequency-domain inference for stationary multivariate Hawkes processes under mild conditions, bridging the gap between theory and applicati…
Change Point Detection and Mean-Field Dynamics of Variable Productivity Hawkes Processes
Conor Kresin, Boris Baeumer, Sophie Phillips
Many self-exciting systems change because endogenous amplification, as opposed to exogenous forcing, varies. We study a Hawkes process with fixed background rate and kernel, but pi…
Multivariate Representations of Univariate Marked Hawkes Processes
Louis Davis, Conor Kresin, Boris Baeumer +1
Univariate marked Hawkes processes are used to model a range of real-world phenomena including earthquake aftershock sequences, contagious disease spread, content diffusion on soci…
A Higher Order Resolvent-positive Finite Difference Approximation for Fractional Derivatives
Boris Baeumer, Mihály Kovács, Matthew Parry
We develop a finite difference approximation of order for the -fractional derivative. The weights of the approximation scheme have the same rate-matrix type properties as…
A Fractional Model for Earthquakes
Louis Davis, Boris Baeumer, Ting Wang
This paper extends the existing fractional Hawkes process to better model mainshock-aftershock sequences of earthquakes. The fractional Hawkes process is a self-exciting point proc…