3 2.3. The embedded discrete-time Hawkes process 5 2.4. Drift of a discrete-time Markov process 6 2.5. A digression on stochastic stability 7 3. Auxiliary Results 8 3.1. V−uniform ergodicity of the intensity of a Hawkes process 8 3.2. V−uniform ergodicity of the intensity of a multivariate Hawkes process 10 3.3. V-uniform ergodicity of a " birth-death " Hawkes process 13 4. Application to order...

In this paper, we shall show that the following translation \(I^M\) from propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic KTB\) is sound: for any formula \(\phi\) and \(\psi\) L_1\), it defined as (M1) \(I^M(\phi \vee \psi) = I^M(\phi) I^M(\psi)\), (M2) \(I^M(\neg \phi) \neg I^M(\phi)\), (M3) \(I^M(\epsilon ab) \Diamond p_a \supset . \wedge \Box p_b .\wedge p_a\), wher...

This work focuses on a class of stochastic damping Hamiltonian systems with state-dependent switching, where the switching process has countably infinite state space. After establishing existence and uniqueness global weak solution via martingale approach under very mild conditions, paper next proves strong Feller property for regime-switching by killing technique together some resolvent transi...

The ergodicity breaking parameter is a measure for the heterogeneity among different trajectories of one ensemble. In this report, this parameter is calculated for fractional Brownian motion with a random change of time scale, often called "subordination." We show that this quantity is the same as the known continuous time random walks case.

A heterostructure composed of $N$ parallel homogeneous layers is studied in the limit as their widths $l_1, \ldots , l_N$ shrink to zero. The problem investigated one dimension and piecewise constant potential Schr\"{o}dinger equation given by strengths $V_1, V_N$ functions l_N$, respectively. key point derivation conditions on $V_1(l_1), V_N(l_N)$ for realizing a family one-point interactions ...

We define a broad class of local Lagrangian intersections which we call quasi-minimally degenerate (QMD) before developing techniques for studying their Floer homology. In some cases, one may think such as modeled on minimally functions defined by Kirwan. One major result this paper is: if $L_0,L_1$ are two submanifolds whose intersection decomposes into QMD sets, there is spectral sequence con...