Band 31, Heft 3

In this paper, we analyze multidimensional generalized backward stochastic differential equations with jumps in a filtration that supports a Brownian motion and an independent integer-valued random measure. Under monotonicity and linear growth assumptions on the coefficients, we give the existence and uniqueness of 𝕃 2 {\mathbb{L}^{2}} -solutions provided that the generators and the terminal condition satisfy some suitable integrability conditions.

We study a Schrödinger random operator where the potential is in terms of a continuous semimartingale. Our model is a generalization of the well-known case where the potential is the white-noise. Our approach is to analyze the random operator by means of its bilinear form. This allows us to construct an inverse operator using an explicit Green kernel. To characterize such homogeneous solutions we use certain stochastic equations in terms of stochastic integrals with respect to the semimartingale. An important tool that we use is the multi-dimensional Itô formula. Also, one important corollary of our results is that the operator has a discrete spectrum.

This paper concerns a class of fractional impulsive neutral functional differential equations with an infinite delay driven by the Rosenblatt process. A set of sufficient conditions are established for the existence of new mild solutions using fixed point theory. Finally, an illustrative example is provided to demonstrate the applicability of the theoretical result.

Skew slash distribution is a distribution which considers both skewness and heavy tail. It is very useful in simulation studies and realistic in representing practical data due to its less peaks, especially in data sets that violate the assumption of normality. In this article, we propose a change-point detection procedure for skew slash distribution based on the modified information criterion (MIC). Meanwhile, we provide an estimation approach based on confidence distribution (CD) to measure the accuracy of change point location estimation. By comparing with the likelihood ratio test, the simulation results show that the MIC-based method performs better in terms of powers, the coverage probabilities and average lengths of confidence sets. In the end, we apply our proposed method to real data and locate the positions of the change points successfully.

The aim of the present paper is to establish some strong stability results for solutions of stochastic differential equations driven by a fractional Brownian sheet with Hurst parameters H , H ′ ∈ ( 0 , 1 ) {H,H^{\prime}\in(0,1)} for which pathwise uniqueness holds.

This paper deals with a class of delay backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than 1 2 {\frac{1}{2}} ). In this type of equation, a generator at time t can depend not only on the present but also on the past solutions. We essentially establish existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout the paper is a divergence-type integral.

In this paper, we introduce a generalization of the two-parameter double Lindley distribution (TPDLD) of Kumar and Jose [C. S. Kumar and R. Jose, A new generalization to Laplace distribution, J. Math. Comput. 31 2020, 8–32], namely the generalized double Lindley distribution (GDLD) along with its location-scale extension (EGDLD). Then we discuss the estimation of parameters of the EGDLD by the maximum likelihood estimation procedure. Next, we illustrate this estimation procedure with the help of certain real life data sets, and a simulation study is carried out to examine the performance of various estimators of the parameters of the distribution.