相关论文: A Note on the Malliavin Differentiability of One-D…

This work focuses on the well-posedness of McKean-Vlasov stochastic differential delay equations. Under suitable lipschitz conditions on the drift and diffusion terms, along with a distribution dependent Lyapunov condition, this paper shows…

We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized…

We consider a stochastic partial differential equation with two logarithmic nonlinearities, with two reflections at 1 and -1 and with a constraint of conservation of the space average. The equation, driven by the derivative in space of a…

In this article, we consider non-smooth time-dependent domains and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic…

We study one-dimensional stochastic integral equations with non-smooth dispersion coefficients, and with drift components that are not restricted to be absolutely continuous with respect to Lebesgue measure. In the spirit of Lamperti, Doss…

We give a proof of the strong existence and the regularity of stochastic differential equations driven by a Brownian motion and a measurable, Markovian drift without no regularity hypothesis except that the Girsanov exponential associated…

We propose an explicit drift-randomised Milstein scheme for both McKean--Vlasov stochastic differential equations and associated high-dimensional interacting particle systems with common noise. By using a drift-randomisation step in space…

Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…

We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and…

In this paper we prove a new strong uniqueness result and a weak existence result for possibly {\it degenerate} multidimensional stochastic differential equations with Sobolev diffusion coefficients and rough drifts. In particular, examples…

This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…

In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…

We introduce a framework for stochastic differential equations (SDEs) with interaction on compact, connected, $d$-dimensional manifolds. For SDEs whose drift and diffusion coefficients may depend on both the state variable and the empirical…

We study SDE $$ d X_t = b(X_t) \, dt + A(X_{t-}) \, d Z_t, \quad X_{0} = x \in \mathbb{R}^d, \quad t \geq 0 $$ where $Z=(Z^1, \dots, Z^d)^T$, with $Z^i, i=1,\dots, d$ being independent one-dimensional symmetric jump L\'evy processes, not…

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…

We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we…

In this paper, we introduce a specific kind of doubly reflected Backward Stochastic Differential Equations (in short DRBSDEs), defined on probability spaces equipped with general filtration that is essentially non quasi-left continuous,…

In this article, we consider a stochastic partial differential equation (SPDE) driven by a L\'evy white noise, with Lipschitz multiplicative term $\sigma$. We prove that under some conditions, this equation has a unique random field…

In this work, we will show the existence, uniqueness, and weak differentiability of the solution to semi-linear mean-field stochastic differential equations driven by fractional Brownian motion. We prove an extension of the…

We introduce an explicit adaptive Milstein method for stochastic differential equations (SDEs) with no commutativity condition. The drift and diffusion are separately locally Lipschitz and together satisfy a monotone condition. This method…