In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribu...In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works;(ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution;(iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Holder continuous) and pathdistribution dependent.展开更多
In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,trunca...In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,truncation method and the Yamada-Watanabe approximation technique,we derived the strong Feller property of the solution.展开更多
We investigate a particle system with mean field interaction living in a random environment characterized by a regime-switching process.The switching process is allowed to be dependent on the particle system.The well-...We investigate a particle system with mean field interaction living in a random environment characterized by a regime-switching process.The switching process is allowed to be dependent on the particle system.The well-posedness and various properties of the limit conditional McKean-Vlasov SDEs are studied,and the conditional propagation of chaos is established with explicit estimate of the convergence rate.展开更多
We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, wher...We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.展开更多
采用同时蒸馏萃取(simultaneous distillation and extraction,SDE),结合气质联用(gas chromatogrophymassspectrometry,GC-MS),对肯德基吮指原味鸡的挥发性风味成分进行分析,并讨论各物质对整体风味的影响。共鉴定出66种化合物,其中烃...采用同时蒸馏萃取(simultaneous distillation and extraction,SDE),结合气质联用(gas chromatogrophymassspectrometry,GC-MS),对肯德基吮指原味鸡的挥发性风味成分进行分析,并讨论各物质对整体风味的影响。共鉴定出66种化合物,其中烃类14种,醛类23种,醇类4种,酮类7种,酚类4种,脂肪酸类3种,酯类2种,内酯类2种,杂环化合物7种。烃类(17.44%)、醛类(45.41%)和脂肪酸类(13.26%)的相对含量较多,其次为酮类(3.65%)、杂环化合物(2.79%)。展开更多
文摘In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works;(ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution;(iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Holder continuous) and pathdistribution dependent.
基金Supported by the National Natural Science Foundation of China(11926322)the Fundamental Research Funds for the Central Universities of South-Central MinZu University(CZY22013,3212023sycxjj001)。
文摘In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,truncation method and the Yamada-Watanabe approximation technique,we derived the strong Feller property of the solution.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11771327,11831014).
文摘We investigate a particle system with mean field interaction living in a random environment characterized by a regime-switching process.The switching process is allowed to be dependent on the particle system.The well-posedness and various properties of the limit conditional McKean-Vlasov SDEs are studied,and the conditional propagation of chaos is established with explicit estimate of the convergence rate.
基金supported by the NSF of China(11071144,11171187,11222110 and 71671104)Shandong Province(BS2011SF010,JQ201202)+4 种基金SRF for ROCS(SEM)Program for New Century Excellent Talents in University(NCET-12-0331)111 Project(B12023)the Ministry of Education of Humanities and Social Science Project(16YJA910003)Incubation Group Project of Financial Statistics and Risk Management of SDUFE
文摘We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.
文摘采用同时蒸馏萃取(simultaneous distillation and extraction,SDE),结合气质联用(gas chromatogrophymassspectrometry,GC-MS),对肯德基吮指原味鸡的挥发性风味成分进行分析,并讨论各物质对整体风味的影响。共鉴定出66种化合物,其中烃类14种,醛类23种,醇类4种,酮类7种,酚类4种,脂肪酸类3种,酯类2种,内酯类2种,杂环化合物7种。烃类(17.44%)、醛类(45.41%)和脂肪酸类(13.26%)的相对含量较多,其次为酮类(3.65%)、杂环化合物(2.79%)。
