相关论文: Distribution of suprema for generalized risk proce…

This paper is devoted to studying the average optimality in continuous-time Markov decision processes with fairly general state and action spaces. The criterion to be maximized is expected average rewards. The transition rates of underlying…

We establish the functional convex order results for two scaled McKean-Vlasov processes $X=(X_{t})_{t\in[0, T]}$ and $Y=(Y_{t})_{t\in[0, T]}$ defined on a filtered probability space $(\Omega, \mathcal{F}, (\mathcal{F}_{t})_{t\geq0},…

We give a dimension-independent sparsification result for suprema of centered Gaussian processes: Let $T$ be any (possibly infinite) bounded set of vectors in $\mathbb{R}^n$, and let $\{\boldsymbol{X}_t := t \cdot \boldsymbol{g} \}_{t\in…

We derive the Markov-modulated generalized Ornstein-Uhlenbeck process by embedding a Markov-modulated random recurrence equation in continuous time. The obtained process turns out to be the unique solution of a certain stochastic…

In extreme value statistics, the peaks-over-threshold method is widely used. The method is based on the generalized Pareto distribution characterizing probabilities of exceedances over high thresholds in $\mathbb {R}^d$. We present a…

In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…

For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…

When modeling a vector of risk variables, extreme scenarios are often of special interest. The peaks-over-thresholds method hinges on the notion that, asymptotically, the excesses over a vector of high thresholds follow a multivariate…

The expected supremum of a Gaussian process indexed by the image of an index set under a function class is bounded in terms of separate properties of the index set and the function class. The bound is relevant to the estimation of nonlinear…

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner's generalized Dirichlet distribution (R.H. Lochner, A Generalized…

In order to describe the extremal behaviour of some stochastic process $X$, approaches from univariate extreme value theory are typically generalized to the spatial domain. In particular, generalized peaks-over-threshold approaches allow…

Let X_t, 0<=t<=T be a one-dimensional stochastic process with independent and stationary increments. This paper considers the problem of stopping the process X_t "as close as possible" to its eventual supremum M_T:=sup{X_t: 0<=t<=T}, when…

In this paper we provide an expansion formula for Hawkes processes which involves the addition of jumps at deterministic times to the Hawkes process in the spirit of the well-known integration by parts formula (or more precisely the Mecke…

Suprema of random processes appear naturally in a plethora of disciplines, and Talagrand's majorizing theorem yields a geometric interpretation for them: for a centered Gaussian random process $(X_t)_{t \in T},$ $\mathbb{E}[\sup_{t \in…

In this paper, we investigate the precise local large deviation probabilities for random sums of independent real-valued random variables with a common distribution $F$, where $F(x+\Delta)=F((x, x+T])$ is an $\mathcal{O}$-regularly varying…

In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…

We study a triple of stochastic processes: a Wiener process $W_t$, $t \geq 0$, its running maxima process $M_t=\sup \{W_s: s \in [0,t]\}$ and its running minima process $m_t=\inf \{W_s: s \in [0,t]\}$. We derive the analytical formulas for…

We consider a refracted jump diffusion process having two-sided jumps with rational Laplace transforms. For such a process, by applying a straightforward but interesting approach, we derive formulas for the Laplace transform of its…

We consider a random process $Y(t)=\exp\{X(t)\}$, where $X(t)$ is a centered second-order process which correlation function $R(t,s)$ can be represented as $\int_{\mathbb{R}} u(t,y)\overline{u(s,y)} dy.$ A multiplicative wavelet-based…

We consider a one-dimensional stationary time series of fixed duration $T$. We investigate the time $t_{\rm m}$ at which the process reaches the global maximum within the time interval $[0,T]$. By using a path-decomposition technique, we…