相关论文: A phase transition for measure-valued SIR epidemic…

We determine the minimal entropy martingale measure for a general class of stochastic volatility models where both price process and volatility process contain jump terms which are correlated. This generalizes previous studies which have…

In this work we investigate the long-time behavior, that is the existence and characterization of invariant measures as well as convergence of transition probabilities, for Markov processes obtained as the unique mild solution to stochastic…

Suppose that $d\geq1$ and $\alpha\in (1, 2)$. Let $Y$ be a rotationally symmetric $\alpha$-stable process on $\R^d$ and $b$ a $\R^d$-valued measurable function on $\R^d$ belonging to a certain Kato class of $Y$. We show that $\rd X^b_t=\rd…

We consider the SIR model and study the first time the number of infected individuals begins to decrease and the first time this population is below a given threshold. We interpret these times as functions of the initial susceptible and…

For each $n\geq 1$, let $ {X_{in}, \quad i \geq 1} $ be independent copies of a nonnegative continuous stochastic process $X_{n}=(X_n(t))_{t\in T}$ indexed by a compact metric space $T$. We are interested in the process of partial maxima…

We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…

Improving the efficiency of discrete time scale invariant (DSI) processes, we consider some flexible sampling of a continuous time DSI process ${X(t), t\in{R^+}}$ with scale $l>1$, which is in correspondence to some multi-dimensional…

Phase transitions in dissipative quantum systems have been investigated using various analytical approaches, particularly in the mean-field (MF) limit. However, analytical results often depend on specific methodologies. For instance,…

In the first part of this thesis, we study a Markov chain on $\mathbb{R}_+ \times S$, where $\mathbb{R}_+$ is the non-negative real numbers and $S$ is a finite set, in which when the $\mathbb{R}_+$-coordinate is large, the $S$-coordinate of…

Define the scaled empirical point process on an independent and identically distributed sequence $\{Y_i: i\le n\}$ as the random point measure with masses at $a_n^{-1} Y_i$. For suitable $a_n$ we obtain the weak limit of these point…

In this paper, we obtain sufficient conditions in terms of projective criteria under which the partial sums of a stationary process with values in ${\mathcal{H}}$ (a real and separable Hilbert space) admits an approximation, in…

The existence of global-in-time bounded martingale solutions to a general class of cross-diffusion systems with multiplicative Stratonovich noise is proved. The equations describe multicomponent systems from physics or biology with…

Most epidemic processes on networks can be modelled by a compartmental model, that specifies the spread of a disease in a population. The corresponding compartmental graph describes how the viral state of the nodes (individuals) changes…

The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking…

In the present paper, a new and simple approach is provided for proving rigorously that for general L\'evy financial markets the minimal entropy martingale measure and the Esscher martingale measure coincide. The method consists in…

We prove that for a so-called sticky process $S$ there exists an equivalent probability $Q$ and a $Q$-martingale $\tilde{S}$ that is arbitrarily close to $S$ in $L^p(Q)$ norm. For continuous $S$, $\tilde{S}$ can be chosen arbitrarily close…

We study the threshold dynamics of a stochastic SAIRS-type model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the epidemic dynamics. In the model, the values of the…

Consider an observation of a multivariate temporal point process $N$ with law $\mathcal P$ on the time interval $[0,T]$. To test the null hypothesis that $\mathcal P$ belongs to a given parametric family, we construct a convergent…

A particular continuous-time multitype branching process is considered, it is the continuous-time embedding of a discrete-time process which is very popular in theoretical computer science: the m-ary search tree (m is an integer). There is…

We study the susceptible-infective-recovered (SIR) epidemic on a random graph chosen uniformly subject to having given vertex degrees. In this model infective vertices infect each of their susceptible neighbours, and recover, at a constant…