Related papers: Rough differential equations with path-dependent c…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
We propose a novel framework for solving continuous-time non-Markovian stochastic control problems by means of neural rough differential equations (Neural RDEs) introduced in Morrill et al. (2021). Non-Markovianity naturally arises in…
Connections between Lie derivatives and the deviation equation has been investigated in spaces with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained…
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…
We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…
In this paper we study rough differential equations driven by Gaussian rough paths from the viewpoint of Malliavin calculus. Under mild assumptions on coefficient vector fields and underlying Gaussian processes, we prove that solutions at a…
We introduce some analytic relations on the set of partial differential equations of two variables. It relies on a new comparison method to give rough asymptotic estimates for solutions which obey different partial differential equations.…
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…
We study a class of linear parabolic path-dependent PDEs (PPDEs) defined on the space of c\`adl\`ag paths $x \in D([0,T])$, in which the coefficient functions at time $t$ depend on $x(t)$ and $\int_{0}^{t}x(s)dA_{s}$, for some…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
The Cauchy-type problem for a nonlinear differential equation involving Hilfer fractional derivative is considered. We prove existence, uniqueness and continuous dependence of a solution for Cauchy-type problem using successive…
We study the inverse problem of parameter identification in non-coercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map by using the first-order and…
We establish two results concerning a class of geometric rough paths $\mathbf{X}$ which arise as Markov processes associated to uniformly subelliptic Dirichlet forms. The first is a support theorem for $\mathbf{X}$ in $\alpha$-H\"older…
We examine the relation between a stochastic version of the rough path integral with the symmetric-Stratonovich integral in the sense of regularization. Under mild regularity conditions in the sense of Malliavin calculus, we establish…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
We study a class of controlled rough differential equations. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the…
The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.
Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Ito map obtained by solving stochastic differential equations. Rough path analysis is about strong regularity of solution to…
Rough stochastic differential equations (rough SDEs), recently introduced by Friz, Hocquet and L\^e in arXiv:2106.10340, have emerged as a versatile tool to study "doubly" SDEs under partial conditioning (with motivation from pathwise…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…