Related papers: Functional differential equations driven by c\`adl…
In this paper, we show that the integration of a stochastic differential equations driven by G-Brownian motion in R can be reduced to the integration of an ordinary differential equations parametrized by a variable in ({\Omega},F). We study…
Using truncated variation techniques we obtain an improved version of the Loeve-Young inequality for the Riemann-Stieltjes integrals driven by rough paths. This allowed us to strenghten some result on the existence of solutions of integral…
We formulate indefinite integration with respect to an irregular function as an algebraic problem and provide a criterion for the existence and uniqueness of a solution. This allows us to define a good notion of integral with respect to…
Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme using a non-linear sewing lemma. In this article,…
Distribution dependent stochastic differential equations have been a very hot subject with extensive studies. On the other hand, under the $G$-expectation framework, stochastic differential equations driven by $G$-Brownian motion (in short…
By using limit theorems of uniform mixing Markov processes and martingale difference sequences, the strong law of large numbers, central limit theorem, and the law of iterated logarithm are established for additive functionals of…
We study a class of stochastic differential equations with non-Lipschitzian coefficients.A unique strong solution is obtained and a large deviation principle of Freidln-Wentzell type has been established.
We investigate existence, uniqueness and approximation of solutions to stochastic delay differential equations (SDDEs) under Carath\'eodory-type drift coefficients. Moreover, we also assume that both drift $f=f(t,x,z)$ and diffusion…
In this paper, we study reflected generalized backward doubly stochastic differential equations driven by Teugels martingales associated with L\'evy process (RGBDSDELs, in short) with one continuous barrier. Under uniformly Lipschitz…
We introduce a differential structure for the space of weakly geometric p rough paths over a Banach space V for 2<p<3. We begin by considering a certain natural family of smooth rough paths and differentiating in the truncated tensor…
This paper investigates existence results for path-dependent differential equations driven by a H{\"o}lder function where the integrals are understood in the Young sense. The two main results are proved via an application of Schauder…
Branched rough paths, defined as paths with values in the character group of the Connes-Kreimer Hopf algebra $\mathcal{H}_\mathrm{CK}$, constitute integration theories that may fail to satisfy the usual integration by parts identity. Using…
This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pertubed linear differential equations obey certain growth or…
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…
We deduce stability and pathwise uniqueness for a McKean-Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Lipschitz drift coefficient and includes moment estimates for…
By using the coupling argument, we establish the Harnack and log-Harnack inequalites for stochastic differential equations with non-Lipschitz drifts and driven by additive anisotropic subordinated Brownian motions (in particular,…
In this work, we introduce a solution theory for scalar-valued rough differential equations driven by multi-indices rough paths. To achieve this task, we will show how the flow approach using the log-ODE method introduced by Bailleul fits…
We show pathwise uniqueness for a class of degenerate It\^{o}-SDE among all of its weak solutions that spend zero time at the points of degeneracy of the dispersion matrix. Consequently, by the Yamada-Watanabe Theorem and a weak existence…
This paper is concerned with the It\^o stochastic differential equations with $\mR^{d\times k}$ diffusions in class of H\"older spaces and continuous $\mR^d$ drifts. We derive a uniqueness result of strong solutions for $\cC^\alpha \…
This paper studies the solvability and the stability of stochastic differential equations driven by G-Brownian motion (GSDEs). In particular, the existence and uniqueness of the solution for locally Lipschitz GSDEs is obtained by…