24 citations · 105 across the 25 of their papers we have counts for
31 papers
Monte Carlo Approximations of Time-Nonlocal Diffusions in Bounded Domains
Ivan Biočić, Daniel E. Cedeño-Girón, Aleksandar Mijatović +1
We develop and analyze a Monte Carlo method for sampling killed anomalous diffusions obtained by time-changing Brownian motion with drift by the inverse of a subordinator. The meth…
Convex minorants and the fluctuation theory of Lévy processes
Jorge Ignacio González Cázares, Aleksandar Mijatović
We establish a novel characterisation of the law of the convex minorant of any Lévy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex…
A Gaussian approximation theorem for Lévy processes
David Bang, Jorge Ignacio González Cázares, Aleksandar Mijatović
Without higher moment assumptions, this note establishes the decay of the Kolmogorov distance in a central limit theorem for Lévy processes. This theorem can be viewed as a continu…
An algorithm for simulating Brownian increments on a sphere
Aleksandar Mijatović, Veno Mramor, Gerónimo Uribe Bravo
This paper presents a novel formula for the transition density of the Brownian motion on a sphere of any dimension and discusses an algorithm for the simulation of the increments o…
Lévy processes on smooth manifolds with a connection
Aleksandar Mijatović, Veno Mramor
We define a Lévy process on a smooth manifold with a connection as a projection of a solution of a Marcus stochastic differential equation on a holonomy bundle of , driven b…
Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation
Jorge González Cázares, Aleksandar Mijatović
We develop a computational method for expected functionals of the drawdown and its duration in exponential Lévy models. It is based on a novel simulation algorithm for the joint la…
Joint density of a stable process and its supremum: regularity and upper bounds
Jorge González Cázares, Arturo Kohatsu Higa, Aleksandar Mijatović
This article uses a combination of three ideas from simulation to establish a nearly optimal polynomial upper bound for the joint density of the stable process and its associated s…
Reflecting random walks in curvilinear wedges
Mikhail V. Menshikov, Aleksandar Mijatović, Andrew R. Wade
We study a random walk (Markov chain) in an unbounded planar domain whose boundary is described by two curves of the form and , with $x_…
Martingale approach to control for general jump processes
Ma. Elena Hernández-Hernández, Saul Jacka, Aleksandar Mijatović
We provide verification theorems (at different levels of generality) for infinite horizon stochastic control problems in continuous time for semimartingales. The control framework…
-strong simulation of the convex minorants of stable processes and meanders
Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
Using marked Dirichlet processes we characterise the law of the convex minorant of the meander for a certain class of Lévy processes, which includes subordinated stable and symmetr…
Invariance principles for local times in regenerative settings
Aleksandar Mijatović, Gerónimo Uribe Bravo
Consider a stochastic process , regenerative at a state which is instantaneous and regular. Let be a regenerative local time for at . Suppos…
Stability of overshoots of zero mean random walks
Aleksandar Mijatović, Vladislav Vysotsky
We prove that for a random walk on the real line whose increments have zero mean and are either integer-valued or spread out (i.e. the distributions of the steps of the walk are ev…
A note on the exact simulation of spherical Brownian motion
Aleksandar Mijatović, Veno Mramor, Gerónimo Uribe Bravo
We describe an exact simulation algorithm for the increments of Brownian motion on a sphere of arbitrary dimension, based on the skew-product decomposition of the process with resp…
Geometrically Convergent Simulation of the Extrema of Lévy Processes
Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
We develop a novel approximate simulation algorithm for the joint law of the position, the running supremum and the time of the supremum of a general Lévy process at an arbitrary f…
Non-asymptotic bounds for sampling algorithms without log-concavity
Mateusz B. Majka, Aleksandar Mijatović, Lukasz Szpruch
Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures. Non-a…
Projections of spherical Brownian motion
Aleksandar Mijatović, Veno Mramor, Gerónimo Uribe Bravo
We obtain a stochastic differential equation (SDE) satisfied by the first coordinates of a Brownian motion on the unit sphere in . The SDE has non-Lipschit…
Invariance principle for non-homogeneous random walks
Nicholas Georgiou, Aleksandar Mijatović, Andrew R. Wade
We prove an invariance principle for a class of zero-drift spatially non-homogeneous random walks in , which may be recurrent in any dimension. The limit $\mathcal{X}…
A radial invariance principle for non-homogeneous random walks
Nicholas Georgiou, Aleksandar Mijatović, Andrew R. Wade
Consider non-homogeneous zero-drift random walks in , , with the asymptotic increment covariance matrix satisfying $\mathbf{u}^\top σ^2 (…
Asymptotic variance for Random walk Metropolis chains in high dimensions: logarithmic growth via the Poisson equation
Aleksandar Mijatović, Jure Vogrinc
There are two ways of speeding up MCMC algorithms: (1) construct more complex samplers that use gradient and higher order information about the target and (2) design a control vari…
On the policy improvement algorithm in continuous time
Saul D. Jacka, Aleksandar Mijatović
We develop a general approach to the Policy Improvement Algorithm (PIA) for stochastic control problems for continuous-time processes. The main results assume only that the control…
On the weak limit law of the maximal uniform k-spacing
Aleksandar Mijatović, Vladislav Vysotsky
This paper gives a simple proof of a limit theorem for the lenght of the largest interval straddling a fixed number of i.i.d. points uniformly disributed on a unit interval. The ke…
Asymptotic independence of three statistics of maximal segmental scores
Aleksandar Mijatović, Martijn Pistorius
Let be an iid sequence with negative mean. The -segment is the subsequence and its \textit{score} is given by $\max\{\sum_{m+1}^nξ_i,0\…
Markov chain approximations to scale functions of Lévy processes
Aleksandar Mijatović, Matija Vidmar, Saul Jacka
We introduce a general algorithm for the computation of the scale functions of a spectrally negative Lévy process , based on a natural weak approximation of via upwards skip…
An integral equation for Root's barrier and the generation of Brownian increments
Paul Gassiat, Aleksandar Mijatović, Harald Oberhauser
We derive a nonlinear integral equation to calculate Root's solution of the Skorokhod embedding problem for atom-free target measures. We then use this to efficiently generate boun…