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pro vyhledávání: '"Haress, El Mehdi"'
We study the numerical approximation of the stochastic heat equation with a distributional reaction term. Under a condition on the Besov regularity of the reaction term, it was proven recently that a strong solution exists and is unique in the pathwi
Externí odkaz:
http://arxiv.org/abs/2405.08201
Autor:
Haress, El Mehdi, Richard, Alexandre
We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equation driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an estimator of t
Externí odkaz:
http://arxiv.org/abs/2306.16272
We study the well-posedness and numerical approximation of multidimensional stochastic differential equations (SDEs) with distributional drift, driven by a fractional Brownian motion. First, we prove weak existence for such SDEs. This holds under a c
Externí odkaz:
http://arxiv.org/abs/2302.11455
Autor:
Haress, El Mehdi, Richard, Alexandre
The fractional Brownian motion can be considered as a Gaussian field indexed by $(t,H)\in { \mathbb{R}_{+} \times (0,1)}$, where $H$ is the Hurst parameter. On compact time intervals, it is known to be almost surely jointly H\"older continuous in tim
Externí odkaz:
http://arxiv.org/abs/2206.06648
Autor:
Holland, Matthew J., Haress, El Mehdi
In this work, we consider the setting of learning problems under a wide class of spectral risk (or "L-risk") functions, where a Lipschitz-continuous spectral density is used to flexibly assign weight to extreme loss values. We obtain excess risk guar
Externí odkaz:
http://arxiv.org/abs/2105.04816
Autor:
Holland, Matthew J., Haress, El Mehdi
We study learning algorithms that seek to minimize the conditional value-at-risk (CVaR), when all the learner knows is that the losses incurred may be heavy-tailed. We begin by studying a general-purpose estimator of CVaR for potentially heavy-tailed
Externí odkaz:
http://arxiv.org/abs/2006.02001
Autor:
Haress, El Mehdi, Hu, Yaozhong
Let the Ornstein-Uhlenbeck process $(X_t)_{t\ge0}$ driven by a fractional Brownian motion $B^{H }$, described by $dX_t = -\theta X_t dt + \sigma dB_t^{H }$ be observed at discrete time instants $t_k=kh$, $k=0, 1, 2, \cdots, 2n+2 $. We propose ergodic
Externí odkaz:
http://arxiv.org/abs/2004.05096
Estimation of all parameters in the fractional Ornstein–Uhlenbeck model under discrete observations.
Autor:
Haress, El Mehdi, Hu, Yaozhong
Publikováno v:
Statistical Inference for Stochastic Processes; Jul2021, Vol. 24 Issue 2, p327-351, 25p