Grusea, Simona Mercier, Sabine

Let A_i, i≥0 be a finite state irreducible aperiodic Markov chain and f a lattice score function such that the average score is negative and positive scores are possible. Define S_0 := 0 and S_k := f(A_1) +...+ f(A_k) the successive partial sums, S^+ the maximal non-negative partial sum, Q_1 the maximal segmental score of the first non-negative exc...

Ould Haye, Mohamedou Philippe, Anne Robet, Caroline

From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly focus on the case when the initial process is Gaussian. The challenge being that, although marginally remains Gaus...

Abi jaber, Eduardo El Euch, Omar

Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to simulate efficiently such models, which makes risk management of derivatives an intricate task. In this paper, we...

Basrak, Bojan Wintenberger, Olivier Zugec, Petra

We study the asymptotic distribution of the total claim amount for marked Poisson cluster models. The marks determine the size and other characteristics of the individual claims and potentially influence arrival rate of the future claims. We find sufficient conditions under which the total claim amount satisfies the central limit theorem or alterna...

Berger, Quentin Salvi, Michele

We consider two models of one-dimensional random walks among biased i.i.d. random conductances: the first is the classical exponential tilt of the conductances, while the second comes from the effect of adding an external field to a random walk on a point process (the bias depending on the distance between points). We study the case when the walk i...

Salvi, Michele Simenhaus, François

We consider a random walk in dimension d ≥ 1 in a dynamic random environment evolving as an interchange process with rate γ > 0. We only assume that the annealed drift is non–zero. We prove that, if we choose γ large enough, almost surely the empirical velocity of the walker Xt/ t eventually lies in an arbitrary small ball around the annealed drift...

Zaplotnik, Luka

Pavlov, Yuri L. Feklistova, Elena V.
Published in
Discrete Mathematics and Applications

We consider configuration graphs with N vertices. The degrees of vertices are independent identically distributed random variables having the power-law distribution with parameter τ > 0. There are two critical values of this parameter: τ = 1 and τ = 2. The properties of a graph change significantly when τ = τ(N) passes these points as N → ∞. Let GN...

Pène, Françoise Thomine, Damien

Z d-extensions of probability-preserving dynamical systems are themselves dynamical systems preserving an infinite measure, and generalize random walks. Using the method of moments, we prove a generalized central limit theorem for additive functionals of the extension of integral zero, under spectral assumptions. As a corollary, we get the fact tha...

Basse-O 'connor, Andreas Lachièze-Rey, Raphaël Podolskij, Mark

In this paper we present some new limit theorems for power variation of kth order increments of stationary increments Lévy driven moving averages. In this infill sampling setting, the asymptotic theory gives very surprising results, which (partially) have no counterpart in the theory of discrete moving averages. More specifically, we will show that...