Uncertain fractional differential equation plays an important role of describing uncertain
dynamic process. This paper focuses on extreme values (including supremum and infimum) …

In this article, we study the forward integral, in the Russo and Vallois sense, with respect to
Hölder continuous stochastic processes Y with exponent bigger than 1∕ 2. Here, the …

We study the numerical approximation of SDEs with singular drifts (including distributions)
driven by a fractional Brownian motion. Under the Catellier–Gubinelli condition that imposes …

We define compositions φ (X) of Hölder paths X in R n and functions of bounded variation φ
under a relative condition involving the path and the gradient measure of φ. We show the …

We prove a result on the fractional Sobolev regularity of composition of paths of low
fractional Sobolev regularity with functions of bounded variation. The result relies on the …

This paper deals with the problem of parameter estimation in a class of stochastic differential
equations driven by a fractional Brownian motion with H≥ 1/2 and a discontinuous …

In this paper, we study a representation for the solutions to sticky stochastic differential
equations driven by a continuous process. The involved stochastic integral is interpreted in …

We study one-dimensional stochastic differential equations of the form $ dX_t=\sigma (X_t)
dY_t $, where $ Y $ is a suitable Hölder continuous driver such as the fractional Brownian …

In this article we introduce and study oscillating Gaussian processes defined by X_t= α _+
Y_t 1 _ Y_t> 0+ α _-Y_t 1 _ Y_t< 0 X t= α+ Y t 1 Y t> 0+ α-Y t 1 Y t< 0, where α _+, α _-> 0 α+ …

In this paper, we combine the techniques of enlargement of filtrations and stochastic control
theory to establish an extension of the verification theorem, where the coefficients of the …