Related papers: Existence and uniqueness for singular stochastic d…
We discuss a concept of path-dependent SDE with distributional drift with possible jumps. We interpret it via a suitable martingale problem, for which we provide existence and uniqueness. The corresponding solutions are expected to be…
We prove the solvability of It\^o stochastic equations with uniformly nondegenerate, bounded, measurable diffusion and drift in $L_{d+1}(\mathbb{R}^{d+1})$. Actually, the powers of summability of the drift in $x$ and $t$ could be different.…
In this paper we are concerned with the stochastic partial differential equations of super-fast diffusion processes describing behavior of plasma dX(t)-{\Delta}ln(X(t)+1)dt=\surd(Q)dW(t), in (0,T)\timesO, where O is a bounded open subset of…
A subdiffusion problem in which the diffusion term is related to a stable stochastic process is introduced. Linear models of these systems have been studied in a general way, but non-linear models require a more specific analysis. The model…
In this paper, we study the existence and uniqueness of solutions to the fully coupled nonlinear forward-backward stochastic differential equations driven by G-Brownian motion. Assuming that the diffusion coefficient $\sigma$ is uniformly…
In this work nonlinear pseudo-differential equations with the infinite number of derivatives are studied. These equations form a new class of equations which initially appeared in p-adic string theory. These equations are of much interest…
We study a higher-dimensional thin film equation that incorporates competitive effects between aggregation and repulsion, where repulsion is modeled by fourth-order diffusion and aggregation by backward second-order degenerate diffusion,…
We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic…
This paper establishes results on the existence and uniqueness of solutions to McKean-Vlasov equations, also called mean-field stochastic differential equations, in an infinite-dimensional Hilbert space setting with irregular drift. Here,…
In this work, we present an effective discrete Edwards-Wilkinson equation aimed to describe the single-file diffusion process. The key physical properties of the system are captured defining an effective elasticity, which is proportional to…
In this paper we focus on the pathwise stability of mild solutions for a class of stochastic partial differential equations which are driven by switching-diffusion processes with jumps. In comparison to the existing literature, we show…
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…
The use of stochastic differential equations in multi-objective optimization has been limited, in practice, by two persistent gaps: incomplete stability analyses and the absence of accessible implementations. We revisit a drift--diffusion…
We consider a generic and explicit tamed Euler--Maruyama scheme for multidimensional time-inhomogeneous stochastic differential equations with multiplicative Brownian noise. The diffusive coefficient is uniformly elliptic, H\"older…
We prove existence and uniqueness for some nonlinear stochastic differential equation used in molecular dynamics, whose nonlinearity comes from a conditional expectation term. We also introduce an interacting particle system in order to…
A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a…
The global-in-time existence and uniqueness of bounded weak solutions to a spinorial matrix drift-diffusion model for semiconductors is proved. Developing the electron density matrix in the Pauli basis, the coefficients (charge density and…
We survey and refine recent results on weak and strong well-posedness of stochastic differential equations with singular drift satisfying some minimal assumptions.
In this paper, we investigate the stochastic differential equation on $\mathbb{R}^d,d\geq2$: \begin{align*} \dif X_t&=v(t,X_t)\dif t+\sqrt{2} \dif W_t. \end{align*} For any finite collection of initial probability measures…
We derive a uniqueness and stability principle for surface diffusion before the onset of singularities. The perturbations, however, are allowed to undergo topological changes. The main ingredient is a relative energy inequality, which in…