Search

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 three different ways. Namely, we deal with Young integral defined by the fractional calculus, and the forward and symmetric integrals in the Russo and Vallois sense. The representation obtained in this paper depends on the amount of time spent by the solution at zero. Hence, we obtain the uniqueness for the solution among the processes that spend zero time at 0. [ABSTRACT FROM AUTHOR]

In this paper, we show the existence and uniqueness of a solution for a stochastic differential equation driven by an additive noise which is the sum of two fractional Brownian motions with different Hurst parameters. The proofs are based on the techniques of fractional calculus and Girsanov theorem. In particular, we show that the regularization effect of the fractional Brownian motion with the smaller Hurst index dominates. A key challenge in this paper is to extend and apply the Girsanov theorem for two noises given by the sum of two (dependent) fractional Brownian motions by using profound techniques of fractional operator theory. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and uniqueness of the mild solution for stochastic Volterra equation with a non-self-adjoint operator. The specific Volterra equation that we consider is a generalization of the fractional differential equation. To obtain the mild solution for the case of multiplicative problem, the resolvent property of the linear perturbation of a sectorial operator will be considered. [ABSTRACT FROM AUTHOR]

In this paper, we establish an averaging principle for neutral stochastic fractional differential equations with non-Lipschitz coefficients and with variable delays, driven by Lévy noise. Our result shows that the solutions of the equations concerned can be approximated by the solutions of averaged neutral stochastic fractional differential equations in the sense of convergence in mean square. As an application, we present an example with numerical simulations to explore the established averaging principle. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of parameter estimation for stochastic differential equations with small fractional Lévy noises, based on discrete observations. Under certain regularity conditions on drift function, the consistency of least squares estimation has been established as a small dispersion coefficient → 0 and the number of discrete points n → ∞ simultaneously. We also obtain the asymptotic behavior of the estimator. [ABSTRACT FROM AUTHOR]

In this paper, we use the techniques of fractional calculus to study the existence of a unique solution to semilinear fractional differential equation driven by a γ -Hölder continuous function 𝜃 with γ ∈ (2 3 , 1). Here, the initial condition is a function that may not be defined at zero and the involved integral with respect to 𝜃 is the extension of the Young integral [An inequality of the Hölder type, connected with Stieltjes integration, Acta Math. 67 (1936) 251–282] given by Zähle [Integration with respect to fractal functions and stochastic calculus I, Probab. Theory Related Fields 111 (1998) 333–374]. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay in Hilbert space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. In the end, we give an example to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the approximation theorem as an averaging principle for the solutions to stochastic fractional differential equations of Itô–Doob type with non-Lipschitz coefficients. The simplified systems will be investigated, and their solutions can be approximated to that of the original systems in the sense of mean square and probability, which constitute the approximation theorem. Two examples are presented with a numerical simulation to illustrate the obtained theory. [ABSTRACT FROM AUTHOR]

In this paper, by using a transformation formula for fractional Brownian motion (fBm), we prove the existence of weak solutions to stochastic differential equations driven by an additive fBm with Hurst parameter 1 / 2 < H < 1 under the linear growth condition. Furthermore, we also consider the uniqueness in law and the pathwise uniqueness of the weak solution. [ABSTRACT FROM AUTHOR]

We prove a conditional local limit theorem for discrete-time fractional Brownian motions (dfBm) with Hurst parameter 3 4 < H < 1. Using results from infinite ergodic theory, it is then shown that the properly scaled occupation time of dfBm converges to a Mittag-Leffler distribution. [ABSTRACT FROM AUTHOR]

In this note we prove that a fractional stochastic delay differential equation which satisfies natural regularity conditions generates a continuous random dynamical system on a subspace of a Hölder space which is separable. [ABSTRACT FROM AUTHOR]