相关论文: Computing sensitivity coefficients in Brownian dyn…

We develop a Malliavin calculus for nonlinear Hawkes processes in the sense of Carlen and Pardoux. This approach, based on perturbations of the jump times of the process, enables the construction of a local Dirichlet form. As an…

By means of the Malliavin calculus, integral representations for the likelihood function and for the derivative of the log-likelihood function are given for a model based on discrete time observations of the solution to equation…

The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift…

Langevin equations are used to model many processes of physical interest, including low-energy nuclear collisions. In this paper we develop a general method for computing probabilities of very rare events (e.g. small fusion cross-sections)…

This paper considers the problem of partially observed optimal control for forward stochastic systems which are driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field…

Fourier acceleration has been successfully applied to the simulation of lattice field theories for more than a decade. In this paper, we extend the method to the dynamics of discrete particles moving in continuum. Although our method is…

Particle approximations for certain nonlinear and nonlocal reaction-diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d. Brownian particles where each particle is…

We consider the problem of Hurst index estimation for solutions of stochastic differential equations driven by an additive fractional Brownian motion. Using techniques of the Malliavin calculus, we analyze the asymptotic behavior of the…

Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs called control variables have to reproduce physical conditions whereas other inputs, called parameters,…

We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the Relative Entropy Rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of…

An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on…

For degenerate stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H>1/2$, the derivative formulas are established by using Malliavin calculus and coupling method, respectively. Furthermore, we find…

We describe a method to extract force and diffusion parameters from single trajectories of Brownian particles based on the principle of maximum likelihood. The analysis is well-suited for out-of-equilibrium trajectories, even when a limited…

We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…

State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…

Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are…

Malliavin calculus is implemented in the context of [M. Hairer, A theory of regularity structures, Invent. Math. 2014]. This involves some constructions of independent interest, notably an extension of the structure which accomodates a…

In this paper we present new theoretical results on optimal estimation of certain random quantities based on high frequency observations of a L\'evy process. More specifically, we investigate the asymptotic theory for the conditional mean…

This paper proposes a generalization of Gaussian mixture models, where the mixture weight is allowed to behave as an unknown function of time. This model is capable of successfully capturing the features of the data, as demonstrated by…

Financial markets have long since been modeled using stochastic methods such as Brownian motion, and more recently, rough volatility models have been built using fractional Brownian motion. This fractional aspect brings memory into the…