This work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters.First,we prove the existence and uniqueness of these equations under non-Lipschitz conditions.Second...This work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters.First,we prove the existence and uniqueness of these equations under non-Lipschitz conditions.Second,we construct maximum likelihood estimators of these parameters and then discuss their strong consistency.Third,a numerical simulation method for the class of path-dependent McKean-Vlasov stochastic differential equations is offered.Finally,we estimate the errors between solutions of these equations and that of their numerical equations.展开更多
This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward-forward systems of equations of mean field games. We present local well-posedness, global ex...This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward-forward systems of equations of mean field games. We present local well-posedness, global existence and some regularity results for these equations.展开更多
We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables （t, x） ∈[0, T]× R^d. Thi...We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables （t, x） ∈[0, T]× R^d. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear Feynman- Kac formula for a general non-Markoviau BSDE. Some main properties of solutions of this new PDEs are also obtained.展开更多
This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonli...This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.展开更多
In this paper,the authors provide a brief introduction of the path-dependent partial differential equations(PDEs for short)in the space of continuous paths,where the path derivatives are in the Dupire(rather than Fr&#...In this paper,the authors provide a brief introduction of the path-dependent partial differential equations(PDEs for short)in the space of continuous paths,where the path derivatives are in the Dupire(rather than Fréchet)sense.They present the connections between Wiener expectation,backward stochastic differential equations(BSDEs for short)and path-dependent PDEs.They also consider the well-posedness of path-dependent PDEs,including classical solutions,Sobolev solutions and viscosity solutions.展开更多
We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations(BSVIEs)with jumps,where path-dependence means the dependence of the free term and generator of a pa...We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations(BSVIEs)with jumps,where path-dependence means the dependence of the free term and generator of a path of a c`adl`ag process.Furthermore,we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation(FSVIE)with jumps and a linear path-dependent BSVIE with jumps.As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.展开更多
Continuous estimation of wrist torque from surface electromyography(EMG) signals has been studied by some research institutes. Hysteresis effect is a phenomenon in EMG force relationship. In this work, a path-dependen...Continuous estimation of wrist torque from surface electromyography(EMG) signals has been studied by some research institutes. Hysteresis effect is a phenomenon in EMG force relationship. In this work, a path-dependent model based on hysteresis effect was used for continuously estimating wrist torque from surface EMG signals. The surface EMG signals of the flexor carpi ulnaris(FCU) and extensor carpi radialis(ECR) were collected along with wrist torque of flexion/extension degree-of-freedom. EMG signal of FCU was used to estimate the torque of wrist flexion and EMG signal of ECR to estimate the torque of wrist extension. The existence of hysteresis effect has been proven either during wrist flexion or extension on all subjects.And the estimation performance of path-dependent model is much better than the overall model. Thus, the path-dependent model is suitable to improve the wrist torque's estimation accuracy.展开更多
基金supported by NSF of China(11001051,11371352,12071071)China Scholarship Council(201906095034).
文摘This work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters.First,we prove the existence and uniqueness of these equations under non-Lipschitz conditions.Second,we construct maximum likelihood estimators of these parameters and then discuss their strong consistency.Third,a numerical simulation method for the class of path-dependent McKean-Vlasov stochastic differential equations is offered.Finally,we estimate the errors between solutions of these equations and that of their numerical equations.
文摘This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward-forward systems of equations of mean field games. We present local well-posedness, global existence and some regularity results for these equations.
基金supported by National Natural Science Foundation of China(Grant No.10921101)the Programme of Introducing Talents of Discipline to Universities of China(Grant No.B12023)the Fundamental Research Funds of Shandong University
文摘We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables （t, x） ∈[0, T]× R^d. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear Feynman- Kac formula for a general non-Markoviau BSDE. Some main properties of solutions of this new PDEs are also obtained.
基金supported by the National Natural Science Foundation of China(Nos.10921101,11471190)the Shandong Provincial Natural Science Foundation of China(No.ZR2014AM002)the Programme of Introducing Talents of Discipline to Universities of China(No.B12023)
文摘This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.
基金supported by the National Key R&D Program of China(Nos.2018YFA0703900,2020YFA0712700,2018YFA0703901)the National Natural Science Foundation of China(Nos.12031009,12171280)the Natural Science Foundation of Shandong Province(Nos.ZR2021YQ01,ZR2022JQ01).
文摘In this paper,the authors provide a brief introduction of the path-dependent partial differential equations(PDEs for short)in the space of continuous paths,where the path derivatives are in the Dupire(rather than Fréchet)sense.They present the connections between Wiener expectation,backward stochastic differential equations(BSDEs for short)and path-dependent PDEs.They also consider the well-posedness of path-dependent PDEs,including classical solutions,Sobolev solutions and viscosity solutions.
文摘We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations(BSVIEs)with jumps,where path-dependence means the dependence of the free term and generator of a path of a c`adl`ag process.Furthermore,we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation(FSVIE)with jumps and a linear path-dependent BSVIE with jumps.As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.
基金National Basic Research Program of Chinagrant number:2011CB013305+1 种基金State Key Laboratory of Robotics and Systemgrant number:SKLRS-2012-ZD-04
文摘Continuous estimation of wrist torque from surface electromyography(EMG) signals has been studied by some research institutes. Hysteresis effect is a phenomenon in EMG force relationship. In this work, a path-dependent model based on hysteresis effect was used for continuously estimating wrist torque from surface EMG signals. The surface EMG signals of the flexor carpi ulnaris(FCU) and extensor carpi radialis(ECR) were collected along with wrist torque of flexion/extension degree-of-freedom. EMG signal of FCU was used to estimate the torque of wrist flexion and EMG signal of ECR to estimate the torque of wrist extension. The existence of hysteresis effect has been proven either during wrist flexion or extension on all subjects.And the estimation performance of path-dependent model is much better than the overall model. Thus, the path-dependent model is suitable to improve the wrist torque's estimation accuracy.
