Journal of Integral Equations and Applications最新文献

{"title":"Reflected BSDEs driven by inhomogeneous simple Lévy processes with RCLL barrier","authors":"M. El Jamali, M. El Otmani","doi":"10.1216/jie.2022.34.201","DOIUrl":"https://doi.org/10.1216/jie.2022.34.201","url":null,"abstract":"In this paper, we study the solution of a backward stochastic differential equation driven by an inhomogeneous simple Lévy process with a rcll reflecting barrier. We show the existence and uniqueness of solution by means of the Snell envelope and the fixed point theorem when the coefficient is stochastic Lipschitz. In term of application, we provide the fair price of the American option in Lévy market. Introduction. The theory of backward stochastic differential equations (BSDEs for short) was developed by Pardoux and Peng [25]. These equations have attracted great interest due to their connections with mathematical finance [10, 8], stochastic control and stochastic games [7, 15, 17, 16]. There have been many studies done on this topic lately, and we can’t talk about those studies without mentioning the Situ’s one [29], which was on BSDEs driven by a Brownian motion and a Poisson point process. In addition to the study of Nualart and Schoutens [24] who have established the existence and uniqueness of solutions for BSDEs driven by a Lévy process. Also, the great study of Bahlali et al. [1] in which they treated the case where the BSDE is driven by a Brownian motion and the martingales of Teugels associated with an independent Lévy process. And last but not least, El Jamali and El Otmani’s [5] in which we have established the existence and uniqueness of solutions for BSDEs driven by an inhomogeneous Lévy processes when the coefficient is stochastic Lipschitz. In the framework of a Brownian filtration, the notion of reflected BSDE has been introduced by ElKaroui et al. [11]. A solution of such an equation that is associated with a coefficient f , terminal value ξ and a barrier L, is a triple process (Y,Z,K) Achieving:  Yt = ξ + ∫ T t f(s, Ys, Zs)ds+KT −Kt − ∫ T t ZsdBs. Yt ≥ Lt P− a.s. for all t ≤ T. The role of the continuous increasing process K is to push upwards the process Y in order to keep it above the barrier with minimal energy, that is, ∫ T 0 (Yt − Lt)dKt = 0. This type of BSDEs is motivated by pricing the American options [9] and studying the mixed game problems [18]. The extension to the cases of reflected BSDE with jumps, which are first, a standard reflected BSDE driven by a Brownian motion and an independent Poisson point process, has been established by Hamadène and Ouknine [19]. Second, Essaky’s [13] studied on the reflected BSDEs with jumps and right continuous left hand limited (rcll for short) obstacle. Third, El Otmani [12] has considered a reflected BSDE driven by a Brownian motion and the martingales of Teugels associated with a pure jump independent Lévy process and rcll obstacle (see e.g. [14, 27, 30]). And last but not least, Lü [23] who treated the case where the reflected BSDE driven by a Brownian motion and the martingales 1991 AMS Mathematics subject classification. 60H20, 60H30, 60J75, 65C30.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49623552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Integrodifferential equations of Volterra type with nonlocal and impulsive conditions","authors":"Amadou Diop, M. Dieye, M. Diop, K. Ezzinbi","doi":"10.1216/jie.2022.34.19","DOIUrl":"https://doi.org/10.1216/jie.2022.34.19","url":null,"abstract":"This work is devoted to the study of a class of nonlocal impulsive integrodifferential equations of Volterra type. We investigate the situation when the resolvent operator corresponding to the linear part of (1) is norm continuous. Our results are obtained by using noncompactness Hausdorff measure and fixed point theorems. An example is provided to illustrate the basic theory of this work.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47825017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fixed point theorems for convex-power condensing operators in Banach algebra","authors":"Sana Hadj Amor, Abdelhak Traiki","doi":"10.1216/jie.2022.34.59","DOIUrl":"https://doi.org/10.1216/jie.2022.34.59","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41630901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mild solution to hybrid fractional differential equations with state-dependent nonlocal conditions","authors":"M. Herzallah, Ashraf H. A. Radwan","doi":"10.1216/jie.2022.34.93","DOIUrl":"https://doi.org/10.1216/jie.2022.34.93","url":null,"abstract":"This paper is devoted to scrutinizing the existence and uniqueness of mild solutions to a hybrid fractional differential equations subject to state-dependent non-local conditions. Special cases of the considered class and the formulated theorems will be displayed. Some examples will be given to illustrate the main results.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48710264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"General decay rate for an abstract weakly dissipative Moore–Gibson–Thompson equation","authors":"J. Hassan, S. Messaoudi","doi":"10.1216/jie.2022.34.75","DOIUrl":"https://doi.org/10.1216/jie.2022.34.75","url":null,"abstract":"In this paper we study an abstract class of weakly dissipative Moore-Gibson-Thompson equation with finite memory. We establish a general decay rate for the solution of the system under some appropriate conditions on the relaxation function.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45584846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiple solutions for a binonlocal fractional p(x,·)-Kirchhoff type problem","authors":"E. Azroul, A. Benkirane, M. Shimi, M. Srati","doi":"10.1216/jie.2022.34.1","DOIUrl":"https://doi.org/10.1216/jie.2022.34.1","url":null,"abstract":"In this paper, we are interested in the multiplicity of weak solutions for a bi-nonlocal fractional p(x, .)-Kirchhoff type problems. Our technical approach is based on the general three critical points theorem obtained by B. Ricceri.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42364554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the solution of a class of integral equations using new weighted convolutions","authors":"R. C. Guerra","doi":"10.1216/jie.2022.34.39","DOIUrl":"https://doi.org/10.1216/jie.2022.34.39","url":null,"abstract":"","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47641538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some new weakly singular nonlinear integral inequalities and their application","authors":"Yaoyao Luo, R. Xu","doi":"10.1216/jie.2021.33.477","DOIUrl":"https://doi.org/10.1216/jie.2021.33.477","url":null,"abstract":"Our purpose of this article is to establish some new weakly singular nonlinear integral inequalities, which generalizes some known integral inequalities. The inequalities given here can be used in the analysis of the qualitative properties of fractional differential equations and integral equations. Applications are also provided to illustrate the usefulness of our results.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44449282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A fast Fourier–Galerkin method solving a system of integral equations for the biharmonic equation","authors":"Bo Wang, D. Yu, Bao Tan","doi":"10.1216/jie.2021.33.511","DOIUrl":"https://doi.org/10.1216/jie.2021.33.511","url":null,"abstract":"In this paper, a fast Fourier-Galerkin method is presented for solving a system of integral equations, which is a reformulation of the Dirichlet problem of the biharmonic equation. This method is based on operator splitting and truncation strategy designing. The truncated matrix has only O(n log n) nonzero entries, but the approximate solutions preserve the stability and optimal convergence order. Numerical examples indicate the theoretical estimate.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42971319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasilinear elliptic systems with nonlinear physical data","authors":"Farah Balaadich, E. Azroul","doi":"10.1216/jie.2021.33.427","DOIUrl":"https://doi.org/10.1216/jie.2021.33.427","url":null,"abstract":"Using the theory of Young measures, we prove the existence of weak solutions to the following quasilinear elliptic system A(u) = f (x)+divσ0(x,u), where A(u) = −divσ(x,u,Du) and f ∈ WLM(Ω;R). This problem corresponds to a diffusion phenomenon with a source f in a moving and dissolving substance, where the motion is described by σ0.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42649932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}