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A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
In this paper, we apply rough paths techniques to provide an approximation of the solution of stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter $H>1/2$. Here, the involved stochastic…
We consider the class of non-linear stochastic partial differential equations studied in \cite{conusdalang}. Equivalent formulations using integration with respect to a cylindrical Brownian motion and also the Skorohod integral are…
In this paper we use the chaos decomposition approach to establish the existence of a unique continuous solution to linear fractional differential equations of the Skorohod type. Here the coefficients are deterministic, the inital condition…
In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter H in (1/4; 1/2). Towards this end, we apply Doss-Sussmann representation of the solution and an…
Strongly consistent and asymptotically normal estimators of the Hurst parameter of solutions of stochastic differential equations are proposed. The estimators are based on discrete observations of the underlying processes.
We study a two-dimensional incompressible vorticity equation on the torus driven by transport-type fractional Brownian noise with Hurst parameter $H \in (1/2,1)$. The model captures persistent, long-range correlated forcing consistent with…
These notes rigorously construct the stochastic integral of a Hilbert Space valued process driven by a Cylindrical Brownian Motion. We expand upon this stochastic calculus to present an introduction to stochastic differential equations in…
We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the…
In this article, we consider the quasi-linear stochastic wave and heat equations on the real line and with an additive Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index $H\in…
We show the existence and uniqueness of strong solutions for stochastic differential equation driven by partial $\alpha$-stable noise and partial Brownian noise with singular coefficients. The proof is based on the regularity of degenerate…
We show that if a random variable is the final value of an adapted log-H\"{o}lder continuous process, then it can be represented as a stochastic integral with respect to a fractional Brownian motion with adapted integrand. In order to…
We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/3,1)$ and multiplicative noise component $\sigma$. When…
This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by H\"older continuous functions with H\"older index greater than $1/2$. The results can be applied to the case of equations…
This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…
We provide a new, concise proof of weak existence and uniqueness of solutions to the stochastic differential equation for the multidimensional skew Brownian motion. We also present an application to Brownian particles with skew-elastic…
The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the…
In this work, we prove a version of H\"{o}rmander's theorem for a stochastic evolution equation driven by a trace-class fractional Brownian motion with Hurst exponent $\frac{1}{2} < H < 1$ and an analytic semigroup on a given separable…
In this work, we will show the existence and uniqueness of the solution to the semi linear stochastic differential equations driven by weighted fractional Brownian motion with delay. We also prove smoothness of the density of the solution…
We study the existence and uniqueness of solutions to stochastic differential equations with Volterra processes driven by L\'evy noise. For this purpose, we study in detail smoothness properties of these processes. Special attention is…