We investigate a two-player non-zero-sum linear-quadratic stochastic differential game under asymmetric information, where the state dynamics is governed by a jump diffusion. The asymmetry in information stems from the structure of the players’ strategies: while one player makes decisions based on full information, the other operates under delayed information due to a time delay in his/her control input. Using the maximum principles and the orthogonal decomposition and reorganization technique, we transform the problem of finding open-loop Nash equilibria to that of solving an auxiliary system of forward-backward stochastic delayed differential equations (FBSDDEs) with mutually orthogonal strategies. Under the assumption of a unique Nash equilibrium, we derive explicit solutions to the auxiliary FBSDDEs and hence obtain an explicit form of the open-loop Nash equilibrium based on a generalized Riccati equation developed in this work. Numerical examples are provided to validate the theoretical results.

Let {Xn}n >= 1 be a sequence of strictly stationary m-dependent random variables with zero means. In this article, we obtain an almost sure central limit theorem for partial sums of m-dependent random variables that are different from standardized partial sums, and by the way, we also establish a central limit theorem for the same. Under suitable conditions, we can also obtain consistent results for self-normalized partial sums.

This paper is concerned with the well-posedness and weak pullback mean random attractors of stochastic p-Laplacian lattice systems driven by superlinear Levy noises. We first prove the existence and uniqueness of solutions of the stchastic system. Based on the global well-posedness of the stochastic system, we define a mean random dynamical system via the solution operators, and then prove the existence and uniqueness of the weak pullback mean random attractors of the mean random dynamical system. Several appropriate stopping times are defined to treat the locally Lipschitz continuity of the discrete p-Laplacian operator as well as the nonlinear drift and diffusion terms. Our results are new even when the growth rate of the Levy noises is reduced to be linear.

In this article, we provide the recursive inequalities for weighted sums of Poisson random variables. Furthermore, we establish their upper and lower bounds. Some numerical simulations are also demonstrated. Particularly, in some cases, we demonstrate that our bounds are sharper than the ones in Pelekis (2016) by numerical results.

Predicting the flow field around sluice gates is essential for controlling water levels and discharges in open channels and rivers. Smooth particle hydrodynamics (SPH) models can satisfactorily reproduce such free-surface flows, but they typically require long computational time and extensive computational resources. In this work, we propose a convolutional neural network (CNN) to predict the flow field around a sluice gate. A validated SPH model is used to carry out extensive simulations, and the generated data set is used to train and test CNN-based models. The results demonstrated that the developed CNN can accurately reproduce sluice gate flows, with R2 values exceeding 90% and significantly reducing the computational costs. Furthermore, various traditional machine learning algorithms comprising adaptive neuro-fuzzy inference system, genetic programing, multigene genetic programing, and one-dimensional CNN were also evaluated, and a comparison of the results showed that the developed CNN performed better than the traditional data-driven algorithms in predicting sluice gate flows. Therefore, the proposed method is a promising tool for providing rapid prediction of the spatial distribution of flow fields near the sluice, and potentially for predicting other spatially distributed hydrologic variables.

In this paper, we consider the ruin probability of risk models with a geometric distribution of claim sizes. Since their probabilities can?t be calculated directly, we use exponential distribution to estimate its upper and lower bounds and asymptotic estimates based on the relationship between geometric distribution and exponential distribution. Finally, some numerical simulations are given to prove the superiority of our estimates.

Rosette-type diffusers are becoming popular nowadays for discharging wastewater effluents. Effluents are known as buoyant jets if they have a lower density than the receiving water, and they are often used for municipal and desalination purposes. These buoyant effluents discharged from rosette-type diffusers are known as rosette-type multiport buoyant discharges. Investigating the mixing properties of these effluents is important for environmental impact assessment and optimal design of the diffusers. Due to the complex mixing and interacting processes, most of the traditional simple methods for studying free single jets become invalid for rosette-type multiport buoyant discharges. Three-dimensional computational fluid dynamics (3D CFD) techniques can satisfactorily model the concentration fields of rosette-type multiport buoyant discharges, but these techniques are typically computationally expensive. In this study, a new technique of simulating rosette-type multiport buoyant discharges using combined 3D CFD and multigene genetic programming (MGGP) techniques is developed. Modeling the concentration fields of rosette-type multiport buoyant discharges using the proposed approach has rarely been reported previously. A validated numerical model is used to carry out extensive simulations, and the generated dataset is used to train and test MGGP-based models. The study demonstrates that the proposed method can provide reasonable predictions and can significantly improve the prediction efficiency.

In this paper, we establish an averaging principle on the infinite time intervals for semilinear stochastic ordinary differential equations with Levy noise. In particular, under suitable conditions we prove that if the coefficients are Poisson stable (including periodic, quasi-periodic, almost periodic, almost automorphic etc), then there exists a unique L-2-bounded solution of the original equation, which inherits the recurrence property of the coefficients, and the recurrent solution uniformly converges to the stationary solution of the averaged equation on the whole real axis in distribution sense.

Existence, uniqueness and asymptotic stability of recurrent solutions have been investigated extensively for semi-linear stochastic differential equations. In this article, we show that the unique recurrent solution depends continuously on the coefficients of the equation in the compact-open topology or uniform topology, which depends on how the coefficients vary with respect to the parameter. For more information see https://ejde.math.txstate.edu/Volumes/2020/113/abstr.html

This article formulates and researches a single-species stochastic population model with Allee effect and Lévy jumps. Firstly, it is shown that the model has a unique global positive solution. Then sufficient conditions for extinction and stochastic permanence are obtained. Finally, the growth rate of the solution is estimated. The results demonstrate that the Lévy jumps could change the properties of the model significantly. Several numerical figures are given to explain the theoretical results.

In this paper, we propose a novel deep learning the based deraining method. The proposed method is motivated by the idea that an effective deraining algorithm should have the ability to remove various remaining rain streaks, which have been processed by the deraining method, in a repeated way. So, we design the deraining network in a coarse-to-fine manner that is multi-stage processing procedure and the parameters are shared in each stage. As the spatial contextual information is important for single image deraining, a densely connected dilation convolution block is proposed to deal with rain streaks with different sizes. Moreover, outer dense connections are used to guide the subsequent deraining procedures by fusing all the previous estimated rain-free images. The quantitative and qualitative experimental results demonstrate the superiority of the proposed method compared with recent state-of-the-art deraining methods on Rain100H, Rain1200, and Rain1400 datasets, while the number of parameters of our proposed method is greatly reduced due to the shared parameters strategy.

We consider non-zero-sum regular-singular stochastic differential games, where the informations available to the two players are asymmetry partial informations. The control strategy of each player consists of two components: regular control and singular control. Applying the Malliavin calculus approach, we establish a necessary maximum principle for the games, where the adjoint processes are explicitly represented by the parameters and the states of the system.

We consider a class of regular–singular stochastic differential games arising in the optimal investment and dividend problem of an insurer under model uncertainty. The information available to the two players is asymmetric partial information and the control variable of each player consists of two components: regular control and singular control. We establish the necessary and sufficient optimality conditions for the saddle point of the zero-sum game. Then, as an application, these conditions are applied to an optimal investment and dividend problem of an insurer under model uncertainty. Furthermore, we generalize our results to the nonzero-sum regular–singular game with asymmetric information, and then the Nash equilibrium point is characterized.

In this paper, we study almost periodic solutions for semilinear stochastic differential equations driven by Lévy noise with exponential dichotomy property. Under suitable conditions on the coefficients, we obtain the existence and uniqueness of bounded solutions. Furthermore, this unique bounded solution is almost periodic in distribution under slightly stronger conditions. We also give two examples to illustrate our results.

and Applied Analysis 3 Fix an open solvency set S ⊂ R. Let τS = inf {t > 0; Y (t) ∉ S} (10) be the bankruptcy time. τS is the first time at which the stochastic process Y(t) exits the solvency set S. Similar optimal control problems in which the terminal time is governed by a stopping criterion are considered in [19–21] in the deterministic case. Let f i : Rk × K → R and g i : Rk → R be given functions, for i = 1, 2. Let A be a family of admissible controls, contained in the set of u(⋅) such that (9) has a unique strong solution and

We study the partial information classical and impulse controls problem of forward-backward systems driven by Lévy processes, where the control variable consists of two components: the classical stochastic control and the impulse control; the information available to the controller is possibly less than the full information, that is, partial information. We derive a maximum principle to give the sufficient and necessary optimality conditions for the local critical points of the classical and impulse controls problem. As an application, we apply the maximum principle to a portfolio optimization problem with piecewise consumption processes and give its explicit solutions.

In this paper, we consider the existence and uniqueness of the solutions which are pseudo almost automorphic in distribution for a class of non-autonomous stochastic differential equations in a Hilbert space. In conclusion, we use the Banach contraction mapping principle and exponential dichotomy property to obtain our main results.

In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy, and the results also hold for some nonlinear equations with the form x′(t) = f(t, x(t)) + λ g (t, x(t)), where f, g are pseudo-almost automorphic functions. We prove our main result by the application of Leray-Schauder fixed point theorem.

We firstly introduce the concept and the properties ofCmalmost periodic functions on time scales, which generalizes the concept of almost periodic functions on time scales and the concept ofC(n)-almost periodic functions. Secondly, we consider the existence and uniqueness of almost periodic solutions for second order dynamic equations on time scales by Schauder’s fixed point theorem and contracting mapping principle. At last, we obtain alternative theorems for second order dynamic equations on time scales.

In this paper, we are concerned with the existence and multiplicity of positive periodic solutions for first-order vector differential equations. By using the Leray-Schauder alternative theorem and the Kransnosel’skii fixed point theorem, we show that the differential equations under the periodic boundary value conditions have at least two positive periodic solutions.