Some properties of a conditioned superdiffusion are investigated. By a basic property we obtain for it, a class of linear additive functionals, so-called weighted occupation time, is studied. At last, we get an intere...Some properties of a conditioned superdiffusion are investigated. By a basic property we obtain for it, a class of linear additive functionals, so-called weighted occupation time, is studied. At last, we get an interesting result about its extinctive property.展开更多
The present work primarily aims to explore the neuronal calcium(Ca^(2+)),IP_(3),and dopamine(DA)signaling systems through a feedback loop model.To date,there has been no exploration of this feedback model in fractiona...The present work primarily aims to explore the neuronal calcium(Ca^(2+)),IP_(3),and dopamine(DA)signaling systems through a feedback loop model.To date,there has been no exploration of this feedback model in fractional-order dynamical systems.This feedback loop model incorporates several crucial mechanisms like the buffering process,IP_(3)-receptor,ryanodine receptor,plasma membrane Ca^(2+)ATPase and sarcoplasmic/endoplasmic reticulum calcium ATPase(SERCA)pump,leak,sodium-calcium exchanger,voltage-gated Ca^(2+)channel,Orai channels,DA-dependent IP_(3)synthesis,and others.By incorporating these mechanisms,the model aims to provide a more comprehensive and realistic understanding of the system under investigation.The present model incorporates fractional-order dynamics along both spatial and temporal dimensions to examine the impacts of superdiffusion and memory showing Brownian motion of Ca^(2+),IP_(3),and DA signaling molecules.The bidirectional feedback between calcium and IP_(3)signaling systems,unidirectional feedback between calcium and dopamine signaling systems,and unidirectional feedback between IP_(3)and dopamine signaling systems have been incorporated into the present model.These feedback loops establish interactions among calcium,IP_(3),and dopamine signaling systems within neuronal cells.The numerical findings were obtained by using the Crank-Nicholson method with the Grunwald technique for fractional space derivatives and the L1method for fractional time derivatives in conjunction with the Gauss-Seidel Iterations.This research specifically investigates the implications of cell memory as well as superdiffusion on Ca^(2+),IP_(3),and DA dynamics in neuronal cells,which are interactive nonlinear systems.The superdiffusion process results in a reduction in Ca^(2+),IP_(3),and DA concentrations,while cellular memory leads to an increase in ion and molecule concentrations in neuronal cells during the initial time.The disruption of any given process can lead to imbalances in calcium,IP_(3),and DA systems,hence contributing to neurotoxicity and cellular demise.展开更多
In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with nonlocal branching mechanisms under a martingale change of measure. As an application of this decomposition,we obtain a neces...In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with nonlocal branching mechanisms under a martingale change of measure. As an application of this decomposition,we obtain a necessary and sufficient condition(called the L log L criterion) for the limit of the fundamental martingale to be non-degenerate. This result complements the related results obtained in Kyprianou et al.(2012),Kyprianou and Murillo-Salas(2013) and Liu et al.(2009) for superprocesses with purely local branching mechanisms and in Kyprianou and Palau(2018) for super Markov chains.展开更多
Suppose X= Xt, XT, Pμis a superdiffusion in ?d with general branching mechanism ψ and general branching rate functionA. We discuss conditions onA to guarantee that the exit measure XTL of the superdiffusionX from bo...Suppose X= Xt, XT, Pμis a superdiffusion in ?d with general branching mechanism ψ and general branching rate functionA. We discuss conditions onA to guarantee that the exit measure XTL of the superdiffusionX from bounded smooth domains in ?d have absolutely continuous states.展开更多
In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with non-local branching mechanisms under a martingale change of measure. As an application of this decomposition, we obtain a nec...In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with non-local branching mechanisms under a martingale change of measure. As an application of this decomposition, we obtain a necessary and sufficient condition (called the L log L criterion) for the limit of the fundamental martingale to be non-degenerate. This result complements the related results obtained in Kyprianou et al.(2012), Kyprianou and Murillo-Salas (2013) and Liu et al.(2009) for superprocesses with purely local branching mechanisms and in Kyprianou and Palau (2018) for super Markov chains.展开更多
Suppose X is a superdiffusion in R^d with general branching mechanism ￠. and Y_(D) denotes the total weighted occupation time of X in a bounded smooth domain D. We discuss the conditions on ψ to guarantee that Y_(D)...Suppose X is a superdiffusion in R^d with general branching mechanism ￠. and Y_(D) denotes the total weighted occupation time of X in a bounded smooth domain D. We discuss the conditions on ψ to guarantee that Y_(D) has absolutey continuous states. And for particular ψ(z) = z^(l+, 0<B ≤1. we prove that. in the case d<2 + 2/B. Y_^(D) is absolutely continuous with respect to the Lebesgue measure in D. whereas in the case d>2 + 2/B. it is singular. As we know the absolute continuity and singularity of Y_(D have not been discussed before.展开更多
The range and the nonextinction property of a supercritical superdiffusion and solutions of its corresponding differential equation are studied. It is proved that under a suitable condition, the conditioned superproce...The range and the nonextinction property of a supercritical superdiffusion and solutions of its corresponding differential equation are studied. It is proved that under a suitable condition, the conditioned superprocess of the supercritical superdiffusion is a subcritical superdiffusion.展开更多
文摘Some properties of a conditioned superdiffusion are investigated. By a basic property we obtain for it, a class of linear additive functionals, so-called weighted occupation time, is studied. At last, we get an interesting result about its extinctive property.
文摘The present work primarily aims to explore the neuronal calcium(Ca^(2+)),IP_(3),and dopamine(DA)signaling systems through a feedback loop model.To date,there has been no exploration of this feedback model in fractional-order dynamical systems.This feedback loop model incorporates several crucial mechanisms like the buffering process,IP_(3)-receptor,ryanodine receptor,plasma membrane Ca^(2+)ATPase and sarcoplasmic/endoplasmic reticulum calcium ATPase(SERCA)pump,leak,sodium-calcium exchanger,voltage-gated Ca^(2+)channel,Orai channels,DA-dependent IP_(3)synthesis,and others.By incorporating these mechanisms,the model aims to provide a more comprehensive and realistic understanding of the system under investigation.The present model incorporates fractional-order dynamics along both spatial and temporal dimensions to examine the impacts of superdiffusion and memory showing Brownian motion of Ca^(2+),IP_(3),and DA signaling molecules.The bidirectional feedback between calcium and IP_(3)signaling systems,unidirectional feedback between calcium and dopamine signaling systems,and unidirectional feedback between IP_(3)and dopamine signaling systems have been incorporated into the present model.These feedback loops establish interactions among calcium,IP_(3),and dopamine signaling systems within neuronal cells.The numerical findings were obtained by using the Crank-Nicholson method with the Grunwald technique for fractional space derivatives and the L1method for fractional time derivatives in conjunction with the Gauss-Seidel Iterations.This research specifically investigates the implications of cell memory as well as superdiffusion on Ca^(2+),IP_(3),and DA dynamics in neuronal cells,which are interactive nonlinear systems.The superdiffusion process results in a reduction in Ca^(2+),IP_(3),and DA concentrations,while cellular memory leads to an increase in ion and molecule concentrations in neuronal cells during the initial time.The disruption of any given process can lead to imbalances in calcium,IP_(3),and DA systems,hence contributing to neurotoxicity and cellular demise.
基金supported by Simons Foundation (Grant No. 520542)a Victor Klee Faculty Fellowship and National Natural Science Foundation of China (Grant No. 11731009)+2 种基金supported by National Natural Science Foundation of China (Grant Nos. 11671017 and 11731009)Key Laboratory of Mathematical Economics and Quantitative Finance (LMEQF) (Peking University),Ministry of Educationsupported by the Simons Foundation (Grant No. #429343)
文摘In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with nonlocal branching mechanisms under a martingale change of measure. As an application of this decomposition,we obtain a necessary and sufficient condition(called the L log L criterion) for the limit of the fundamental martingale to be non-degenerate. This result complements the related results obtained in Kyprianou et al.(2012),Kyprianou and Murillo-Salas(2013) and Liu et al.(2009) for superprocesses with purely local branching mechanisms and in Kyprianou and Palau(2018) for super Markov chains.
文摘Suppose X= Xt, XT, Pμis a superdiffusion in ?d with general branching mechanism ψ and general branching rate functionA. We discuss conditions onA to guarantee that the exit measure XTL of the superdiffusionX from bounded smooth domains in ?d have absolutely continuous states.
文摘In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with non-local branching mechanisms under a martingale change of measure. As an application of this decomposition, we obtain a necessary and sufficient condition (called the L log L criterion) for the limit of the fundamental martingale to be non-degenerate. This result complements the related results obtained in Kyprianou et al.(2012), Kyprianou and Murillo-Salas (2013) and Liu et al.(2009) for superprocesses with purely local branching mechanisms and in Kyprianou and Palau (2018) for super Markov chains.
基金This work is supported by NNSF of China(Grant No. 19801019)China Postdoctoral Foundation
文摘Suppose X is a superdiffusion in R^d with general branching mechanism ￠. and Y_(D) denotes the total weighted occupation time of X in a bounded smooth domain D. We discuss the conditions on ψ to guarantee that Y_(D) has absolutey continuous states. And for particular ψ(z) = z^(l+, 0<B ≤1. we prove that. in the case d<2 + 2/B. Y_^(D) is absolutely continuous with respect to the Lebesgue measure in D. whereas in the case d>2 + 2/B. it is singular. As we know the absolute continuity and singularity of Y_(D have not been discussed before.
文摘The range and the nonextinction property of a supercritical superdiffusion and solutions of its corresponding differential equation are studied. It is proved that under a suitable condition, the conditioned superprocess of the supercritical superdiffusion is a subcritical superdiffusion.
