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This study focuses on large deviation principles for fully coupled multiscale multivalued stochastic systems, in which the slow component is governed by a multivalued stochastic differential equation and the fast component is described by a…

Probability · Mathematics 2025-12-12 Huijie Qiao

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

This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of…

Fluid Dynamics · Physics 2025-03-21 Arnaud Debussche , Etienne Mémin

We establish a large deviation principle for a reflected Poisson driven SDE. Our motivation is to study in a forthcoming paper the problem of exit of such a process from the basin of attraction of a locally stable equilibrium associated…

Probability · Mathematics 2020-03-09 Etienne Pardoux , Brice Samegni-Kepgnou

We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed…

Pricing of Securities · Quantitative Finance 2011-07-29 Mikhail Martynov , Olga Rozanova

We study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper…

Probability · Mathematics 2022-09-15 Giulia Catalini , Barbara Pacchiarotti

In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…

Dynamical Systems · Mathematics 2017-09-15 Getachew K. Befekadu

In this paper, we study small noise asymptotics of Markov-modulated diffusion processes in the regime that the modulating Markov chain is rapidly switching. We prove the joint sample-path large deviations principle for the Markov-modulated…

Probability · Mathematics 2023-02-27 Gang Huang , Michel Mandjes , Peter Spreij

Over the recent past data-driven algorithms for solving stochastic optimal control problems in face of model uncertainty have become an increasingly active area of research. However, for singular controls and underlying diffusion dynamics…

Optimization and Control · Mathematics 2024-10-15 Sören Christensen , Asbjørn Holk Thomsen , Lukas Trottner

In this article we establish a large deviation principle for the family {\nu_{\epsilon}:\epsilon \in (0,1)} of distributions of the scaled stochastic processes {P_{-\log\sqrt{\epsilon}}Z_t}_{t\leq 1}, where (Z_t)_{t\in \lbrack 0,1]} is a…

Probability · Mathematics 2009-04-06 Z. Qian , C. Xu

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

Statistical Mechanics · Physics 2011-09-09 Guy Fayolle , Cyril Furtlehner

We consider a transformed Ornstein-Uhlenbeck process model that can be a good candidate for modelling real-life processes characterized by a combination of time-reverting behaviour with heavy distribution tails. We begin with presenting the…

Probability · Mathematics 2011-03-01 K. Borovkov , G. Decrouez

Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer…

Statistical Finance · Quantitative Finance 2013-11-19 Raoul Golan , Austin Gerig

We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options.…

Pricing of Securities · Quantitative Finance 2016-04-06 Peter Friz , Stefan Gerhold , Arpad Pinter

Using the large-deviation formalism, we study the statistics of current fluctuations in a diffusive nonequilibrium quantum spin chain. The boundary-driven XX chain with dephasing consists of a coherent bulk hopping and a local dissipative…

Statistical Mechanics · Physics 2014-04-25 Marko Znidaric

For the Ornstein-Uhlenbeck process, the asymptotic behavior of the maximum likelihood estimator of the drift parameter is totally different in the stable, unstable, and explosive cases. Notwithstanding of this trichotomy, we investigate…

Probability · Mathematics 2011-11-28 Bernard Bercu , Laure Coutin , Nicolas Savy

We establish a diffusion approximation for a class of multi-agent controlled queueing systems, demonstrating their convergence to a system of interacting reflected Ornstein--Uhlenbeck (OU) processes. The limiting process captures essential…

Probability · Mathematics 2026-01-12 Thoa Thieu , Roderick Melnik

The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state…

Mathematical Finance · Quantitative Finance 2025-10-13 Nicola F. Zaugg , Lech A. Grzelak

This paper mainly investigates reflected stochastic recursive control problems governed by jump-diffusion dynamics. The system's state evolution is described by a stochastic differential equation driven by both Brownian motion and Poisson…

Optimization and Control · Mathematics 2025-05-15 Lu Liu , Qingmeng Wei

We obtain large deviation results for a two time-scale model of jump-diffusion processes. The processes on the two time scales are fully inter-dependent, the slow process has small perturbative noise and the fast process is ergodic. Our…

Probability · Mathematics 2016-09-19 Rohini Kumar , Lea Popovic