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This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method…

Probability · Mathematics 2025-09-16 Wenting Xu , Yong Xu , Xiaoyu Yang , Bin Pei

In this article, we establish the Freidlin-Wentzell type large deviation principle and central limit theorem for stochastic fractional conservation laws with small multiplicative noise in kinetic formulation framework. The weak convergence…

Probability · Mathematics 2023-06-08 Soumya Ranjan Behera , Ananta K. Majee

A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a…

Probability · Mathematics 2010-01-28 Wei Wang , A. J. Roberts , Jinqiao Duan

We investigate the Large Deviation behavior in small time of continuous Gaussian processes. We introduce a general procedure allowing to derive Large Deviation Principles in small time starting from the well understood context of Large…

Probability · Mathematics 2023-01-11 Paolo Baldi , Barbara Pacchiarotti

We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of driven semimartingales, so that if the noise-control pairs…

Probability · Mathematics 2024-08-13 Qiao Huang , Wei Wei , Jinqiao Duan

We consider the short time behaviour of stochastic systems affected by a stochastic volatility evolving at a faster time scale. We study the asymptotics of a logarithmic functional of the process by methods of the theory of homogenisation…

Analysis of PDEs · Mathematics 2014-05-14 Martino Bardi , Annalisa Cesaroni , Daria Ghilli

We prove large deviation principles for $\int_0^t \gamma(X_s)ds$, where $X$ is a $d$-dimensional self-similar Gaussian process and $\gamma(x)$ takes the form of the Dirac delta function $\delta(x)$, $|x|^{-\beta}$ with $\beta\in (0,d)$, or…

Probability · Mathematics 2020-01-22 Xiaoming Song

Realized statistics based on high frequency returns have become very popular in financial economics. In recent years, different non-parametric estimators of the variation of a log-price process have appeared. These were developed by many…

Probability · Mathematics 2014-11-20 Hacène Djellout , Arnaud Guillin , Yacouba Samoura

We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof…

Probability · Mathematics 2010-12-14 Magdalena Kobylanski

The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…

Pricing of Securities · Quantitative Finance 2019-08-02 Raul Merino , Jan Pospíšil , Tomáš Sobotka , Tommi Sottinen , Josep Vives

In this paper, we are concerned with multi-scale distribution dependent stochastic differential equations driven by fractional Brownian motion (with Hurst index $H>\frac12$ and standard Brownian motion, simultaneously. Our aim is to…

Probability · Mathematics 2023-06-12 Shen Gunagjun , Zhou Huan , Wu Jianglun

Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of…

Statistical Finance · Quantitative Finance 2014-10-14 Jim Gatheral , Thibault Jaisson , Mathieu Rosenbaum

In this paper, we consider a kind of fully coupled slow fast motion, in which the slow variable satisfies the non Lipschitz condition. We prove that the stochastic flow of the slow variable exists and moreover, satisfies the large deviation…

Probability · Mathematics 2024-09-20 Mingkun Ye , Zuozheng Zhang

In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…

Probability · Mathematics 2013-01-29 Konstantinos Spiliopoulos

We demonstrate the large deviation property for the mild solutions of stochastic evolution equations with monotone nonlinearity and multiplica- tive noise. This is achieved using the recently developed weak convergence method, in studying…

Probability · Mathematics 2010-03-17 Hassan Dadashi-Arani , Bijan Z. Zangeneh

For a fractional Brownian motion $B^H$ with Hurst parameter $H\in]{1/4},{1/2}[\cup]{1/2},1[$, multiple indefinite integrals on a simplex are constructed and the regularity of their sample paths are studied. Then, it is proved that the…

Probability · Mathematics 2007-05-23 Marta Sanz-Solé , Iván Torrecilla-Tarantino

We demonstrate the large deviation principle in the small noise limit for the mild solution of stochastic evolution equations with monotone nonlinearity. A recently developed method, weak convergent method, has been employed in studying the…

Probability · Mathematics 2013-09-10 Hassan Dadashi

We propose a new class of rough stochastic volatility models obtained by modulating the power-law kernel defining the fractional Brownian motion (fBm) by a logarithmic term, such that the kernel retains square integrability even in the…

Mathematical Finance · Quantitative Finance 2021-05-04 Christian Bayer , Fabian Andsem Harang , Paolo Pigato

This work is devoted to studying asymptotic behaviors for Volterra type McKean-Vlasov stochastic differential equations with small noise. By applying the weak convergence approach, we establish the large and moderate deviation principles.…

Probability · Mathematics 2024-10-11 Shanqi Liu , Yaozhong Hu , Hongjun Gao

The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid…

Probability · Mathematics 2022-12-13 Ankit Kumar , Manil T. Mohan