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This article is concerned with the multilevel Monte Carlo (MLMC) methods for approximating expectations of some functions of the solution to the Heston 3/2-model from mathematical finance, which takes values in $(0, \infty)$ and possesses…

Numerical Analysis · Mathematics 2024-03-12 Xiaojuan Wu , Siqing Gan

We design numerical schemes for a class of slow-fast systems of stochastic differential equations, where the fast component is an Ornstein-Uhlenbeck process and the slow component is driven by a fractional Brownian motion with Hurst index…

Probability · Mathematics 2021-04-30 Charles-Edouard Bréhier

Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…

Optimization and Control · Mathematics 2025-09-10 Jingfan Xia , Zhenwei Lin , Qi Deng

We consider a unifying framework for stochastic control problem including the following features: partial observation, path-dependence (both with respect to the state and the control), and without any non-degeneracy condition on the…

Probability · Mathematics 2016-09-14 Elena Bandini , Andrea Cosso , Marco Fuhrman , Huyên Pham

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

Computation · Statistics 2012-05-03 Umberto Picchini , Susanne Ditlevsen

The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…

Machine Learning · Statistics 2025-08-18 Arnab Ganguly , Riten Mitra , Jinpu Zhou

In this paper, the distribution dependent stochastic differential equation in a separable Hilbert space with a Dini continuous drift is investigated. The existence and uniqueness of weak and strong solutions are obtained. Moreover, some…

Probability · Mathematics 2020-04-21 Xing Huang , Yulin Song

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…

Machine Learning · Statistics 2020-06-29 Martin Jørgensen , Marc Peter Deisenroth , Hugh Salimbeni

This paper is concerned with the existence and uniqueness of random periodic solutions for stochastic differential equations (SDEs), where the drift terms involved need not to be uniformly dissipative. On the one hand, via the reflection…

Probability · Mathematics 2025-05-28 Jianhai Bao , Yue Wu

In this paper, we introduce adaptive Euler-Maruyama schemes for McKean-Vlasov stochastic differential equations (SDEs) assuming only a standard monotonicity condition on the drift and diffusion coefficients but no global Lipschitz…

Numerical Analysis · Mathematics 2021-11-02 Christoph Reisinger , Wolfgang Stockinger

In the present article we study strong approximation of solutions of scalar stochastic differential equations (SDEs) with bounded and $\alpha$-H\"older continuous drift coefficient and constant diffusion coefficient at time point $1$.…

Probability · Mathematics 2025-04-30 Simon Ellinger , Thomas Müller-Gronbach , Larisa Yaroslavtseva

We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…

Statistics Theory · Mathematics 2021-09-20 Teppei Ogihara , Mitja Stadje

Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. The…

Numerical Analysis · Mathematics 2011-11-18 Martin Hutzenthaler , Arnulf Jentzen

In this paper, the Milstein method is used to approximate invariant measures of stochastic differential equations with commutative noise. The decay rate of the transition probability kernel generated by the Milstein method to the unique…

Numerical Analysis · Mathematics 2019-01-28 Lihui Weng , Wei Liu

The mean-field stochastic partial differential equation (SPDE) corresponding to a mean-field super-Brownian motion (sBm) is obtained and studied. In this mean-field sBm, the branching-particle lifetime is allowed to depend upon the…

Probability · Mathematics 2022-12-13 Yaozhong Hu , Michael A. Kouritzin , Panqiu Xia , Jiayu Zheng

We consider numerical schemes for computing the linear response of steady-state averages of stochastic dynamics with respect to a perturbation of the drift part of the stochastic differential equation. The schemes are based on Girsanov's…

Numerical Analysis · Mathematics 2019-12-18 Petr Plechac , Gabriel Stoltz , Ting Wang

The challenging problem of conducting fully Bayesian inference for the reaction rate constants governing stochastic kinetic models (SKMs) is considered. Given the challenges underlying this problem, the Markov jump process representation is…

Computation · Statistics 2019-01-10 Andrew Golightly , Emma Bradley , Tom Lowe , Colin S. Gillespie

We propose a hybrid algorithm for the time integration of large sets of rate equations coupled by a relatively small number of degrees of freedom. A subset containing fast degrees of freedom evolves deterministically, while the rest of the…

Materials Science · Physics 2015-06-16 Marco Gherardi , Thomas Jourdan , Solène Le Bourdiec , Guy Bencteux

A new, improved split-step backward Euler (SSBE) method is introduced and analyzed for stochastic differential delay equations(SDDEs) with generic variable delay. The method is proved to be convergent in mean-square sense under conditions…

Numerical Analysis · Mathematics 2011-07-05 Xiaojie Wang , Siqing Gan

This paper considers the problem of minimizing the time average of a controlled stochastic process subject to multiple time average constraints on other related processes. The probability distribution of the random events in the system is…

Optimization and Control · Mathematics 2016-12-20 Xiaohan Wei , Hao Yu , Michael J. Neely