wanyu/IteraTeR_full_sent huggingface dataset:
Original:  The proposed formalism is illustrated through its implementation on an example network. Simulations show that continuous results are produced, thus allowing fine analysis, and that modulating the signal conveyed by the edges allows their tuning according to knowledge about the interaction they model.
Revised:  The proposed formalism is illustrated through its implementation on a tiny sample of the epidermal growth factor receptor signaling pathway. The obtained simulations show that continuous results are produced, thus allowing fine analysis, and that modulating the signal conveyed by the edges allows their tuning according to knowledge about the interaction they model.
Edit intent: meaning-changed
Original:  Simulations show that continuous results are produced, thus allowing fine analysis, and that modulating the signal conveyed by the edges allows their tuning according to knowledge about the interaction they model. The present work is expected to bring enhancements in the ability of qualitative models to simulate biological networks .
Revised:  Simulations show that continuous results are produced, thus allowing fine analysis, and that modulating the signal conveyed by the edges allows their tuning according to knowledge about the modeled interactions, thus incorporating more knowledge. The proposed modeling approach is expected to bring enhancements in the ability of qualitative models to simulate biological networks .
Edit intent: meaning-changed
Original:  Together with the use of other COMBINE standard formats , OMEX is the basis of the COMBINE archive , a single file that supports the exchange of all the information necessary for a modeling and simulation experiment in biology.
Revised:  Together with the use of other standard formats from the Computational Modeling in Biology Network (COMBINE) , OMEX is the basis of the COMBINE archive , a single file that supports the exchange of all the information necessary for a modeling and simulation experiment in biology.
Edit intent: meaning-changed
Original:  Together with the use of other COMBINE standard formats , OMEX is the basis of the COMBINE archive , a single file that supports the exchange of all the information necessary for a modeling and simulation experiment in biology.
Revised:  Together with the use of other COMBINE standard formats , OMEX is the basis of the COMBINE Archive , a single file that supports the exchange of all the information necessary for a modeling and simulation experiment in biology.
Edit intent: fluency
Original:  We anticipate that the COMBINE archive will become a significant help  , as the domain moves to larger, more complex experiments such as multi-scale models URLans, URLanisms, and bioengineering.
Revised:  We anticipate that the COMBINE Archive will become a significant help , as the domain moves to larger, more complex experiments such as multi-scale models URLans, URLanisms, and bioengineering.
Edit intent: fluency
Original:  We anticipate that the COMBINE archive will become a significant help  , as the domain moves to larger, more complex experiments such as multi-scale models URLans, URLanisms, and bioengineering.
Revised:  We anticipate that the COMBINE archive will become a significant help for modellers , as the domain moves to larger, more complex experiments such as multi-scale models URLans, URLanisms, and bioengineering.
Edit intent: meaning-changed
Original: On a filtered probability space (\Omega,\mathcal{F,P,F=(F_t)_{0\leq t\leq T}), we consider stopper-stopper games }%DIFDELCMD < \bar %%% C:
Revised: ,P,F=(F_t)_{0\leq t\leq T}), we consider stopper-stopper games }%DIFDELCMD < \bar %%% C:
Edit intent: meaning-changed
Original: On a filtered probability space (\Omega,\mathcal{F,P,F=(F_t)_{0\leq t\leq T}), we consider stopper-stopper games }%DIFDELCMD < \bar %%% C:=\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Revised: On a filtered probability space (\Omega,\mathcal{F,P,F=(F_t)_{0\leq t\leq T}), we consider stopper-stopper games }%DIFDELCMD < \bar %%% \tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Edit intent: coherence
Original: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Revised: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% %DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Edit intent: fluency
Original: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Revised: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% \rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Edit intent: coherence
Original: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Revised: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% _{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Edit intent: meaning-changed
Original: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Revised: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% We consider a zero-sum continuous time stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Edit intent: meaning-changed
Original: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Revised: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping %DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Edit intent: fluency
Original: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Revised: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% %DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Edit intent: fluency
Original: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Revised: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% %DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Edit intent: fluency
Original: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Revised: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% %DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions.
Edit intent: coherence
Original: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions. We show that%DIFDELCMD < \bar %%% C=%DIFDELCMD < \underline %%% C, by converting these problems into a corresponding Dynkin game  .
Revised: =\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% %DIFDELCMD < \bar %%% C=%DIFDELCMD < \underline %%% C, by converting these problems into a corresponding Dynkin game .
Edit intent: meaning-changed
Original:  We show that%DIFDELCMD < \bar %%% C=%DIFDELCMD < \underline %%% C, by converting these problems into a corresponding Dynkin game  .
Revised:  We show that%DIFDELCMD < \bar %%% C=%DIFDELCMD < \underline %%% C, by converting these problems into a corresponding Dynkin game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games .
Edit intent: meaning-changed
Original:  In addition to increasing the detective quantum efficiency with which images can be recorded , acquisition of DDD movies during exposures allows for correction of movement of the specimen, due both to instabilities in the specimen stage of the microscope and electron beam-induced movement.
Revised:  In addition to an improved camera detective quantum efficiency with which images can be recorded , acquisition of DDD movies during exposures allows for correction of movement of the specimen, due both to instabilities in the specimen stage of the microscope and electron beam-induced movement.
Edit intent: clarity
Original:  In addition to increasing the detective quantum efficiency with which images can be recorded , acquisition of DDD movies during exposures allows for correction of movement of the specimen, due both to instabilities in the specimen stage of the microscope and electron beam-induced movement.
Revised:  In addition to increasing the detective quantum efficiency , acquisition of DDD movies during exposures allows for correction of movement of the specimen, due both to instabilities in the specimen stage of the microscope and electron beam-induced movement.
Edit intent: clarity
Original:  In addition to increasing the detective quantum efficiency with which images can be recorded , acquisition of DDD movies during exposures allows for correction of movement of the specimen, due both to instabilities in the specimen stage of the microscope and electron beam-induced movement.
Revised:  In addition to increasing the detective quantum efficiency with which images can be recorded , acquisition of DDD movies allows for correction of movement of the specimen, due both to instabilities in the specimen stage of the microscope and electron beam-induced movement.
Edit intent: clarity
Original:  In addition to increasing the detective quantum efficiency with which images can be recorded , acquisition of DDD movies during exposures allows for correction of movement of the specimen, due both to instabilities in the specimen stage of the microscope and electron beam-induced movement.
Revised:  In addition to increasing the detective quantum efficiency with which images can be recorded , acquisition of DDD movies during exposures allows for correction of movement of the specimen, due both to instabilities in the microscope specimen stage and electron beam-induced movement.
Edit intent: fluency
Original:  Algorithms have already been described that can correct movement of entire frames or large regions of frames at exposures of 2-3 e^{- rolling averages to be calculated from frames and fit linear trajectories for particles.
Revised:  Algorithms have already been described that can correct movement for large regions of frames at exposures of 2-3 e^{- rolling averages to be calculated from frames and fit linear trajectories for particles.
Edit intent: clarity
Original:  Algorithms have already been described that can correct movement of entire frames or large regions of frames at exposures of 2-3 e^{- rolling averages to be calculated from frames and fit linear trajectories for particles.
Revised:  Algorithms have already been described that can correct movement of entire frames or large regions of frames and for > 1 MDa protein particles. Another algorithm allows individual < 1 MDa protein particle trajectories to be estimated, but requires rolling averages to be calculated from frames and fit linear trajectories for particles.
Edit intent: meaning-changed
Original:  Algorithms have already been described that can correct movement of entire frames or large regions of frames at exposures of 2-3 e^{- rolling averages to be calculated from frames and fit linear trajectories for particles.
Revised:  Algorithms have already been described that can correct movement of entire frames or large regions of frames at exposures of 2-3 e^{- rolling averages to be calculated from frames and fits linear trajectories for particles.
Edit intent: fluency
Original:  Here we describe an algorithm that allows for individual < 1 MDa particle images to be aligned without frame averaging when imaged with 2.5 e^{- . The algorithm maximizes the overall correlation of the shifted frames with the sum of the shifted frames.
Revised:  Here we describe an algorithm that allows for individual < 1 MDa particle images to be aligned without frame averaging or linear trajectories . The algorithm maximizes the overall correlation of the shifted frames with the sum of the shifted frames.
Edit intent: meaning-changed
Original:  DDD movies of the\textit{Saccharomyces cerevisiae V-ATPase are used to demonstrate that the algorithm is able to produce physically reasonable trajectories for a 900 kDa membrane protein complex .
Revised:  \textit{Saccharomyces cerevisiae V-ATPase are used to demonstrate that the algorithm is able to produce physically reasonable trajectories for a 900 kDa membrane protein complex .
Edit intent: clarity
Original:  DDD movies of the\textit{Saccharomyces cerevisiae V-ATPase are used to demonstrate that the algorithm is able to produce physically reasonable trajectories for a 900 kDa membrane protein complex .
Revised:  DDD movies of the\textit{ V-ATPase are used to demonstrate that the algorithm is able to produce physically reasonable trajectories for a 900 kDa membrane protein complex .
Edit intent: meaning-changed
Original:  DDD movies of the\textit{Saccharomyces cerevisiae V-ATPase are used to demonstrate that the algorithm is able to produce physically reasonable trajectories for a 900 kDa membrane protein complex .
Revised:  DDD movies of the\textit{Saccharomyces cerevisiae This individual particle motion correction, in combination with weighting of Fourier components to account for increasing radiation damage in later frames, can be used to improve 3-D maps from single particle cryo-EM .
Edit intent: meaning-changed
Original:  Effects of removing edges with high {\cal P}_e might initially seem inconspicuous but is eventually shown to be very harmful for the network. When compared to existing strategies,  removal of edges by {\cal P}_e , leads to remarkable increase of diameter and average  path length in  real and random networks till the first disconnection and  beyond.
Revised:  Effects of removing edges with high {\cal P}_e might initially seem inconspicuous but is eventually shown to be very harmful for networks. Compared to existing strategies, removal of edges by {\cal P}_e , leads to remarkable increase of diameter and average path length in real and random networks till the first disconnection and beyond.
Edit intent: coherence
Original:  When compared to existing strategies,  removal of edges by {\cal P}_e , leads to remarkable increase of diameter and average  path length in  real and random networks till the first disconnection and  beyond.
Revised:  When compared to existing strategies, removal of edges by {\cal P}_e , leads to remarkable increase of diameter and average path length in undirected real and random networks till the first disconnection and beyond.
Edit intent: meaning-changed
Original: This paper studies Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space ( namely, a Borel right process (BRP)) and the pricing kernel ( stochastic discount factor , state-price density ) is a positive semimartingale multiplicative functional of X.
Revised: This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space ( namely, a Borel right process (BRP)) and the pricing kernel ( stochastic discount factor , state-price density ) is a positive semimartingale multiplicative functional of X.
Edit intent: meaning-changed
Original: This paper studies Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space ( namely, a Borel right process (BRP)) and the pricing kernel ( stochastic discount factor , state-price density ) is a positive semimartingale multiplicative functional of X.
Revised: This paper studies Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space ( Borel right process (BRP)) and the pricing kernel ( stochastic discount factor , state-price density ) is a positive semimartingale multiplicative functional of X.
Edit intent: clarity
Original: This paper studies Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space ( namely, a Borel right process (BRP)) and the pricing kernel ( stochastic discount factor , state-price density ) is a positive semimartingale multiplicative functional of X.
Revised: This paper studies Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space ( namely, a Borel right process (BRP)) and the stochastic discount factor , state-price density ) is a positive semimartingale multiplicative functional of X.
Edit intent: clarity
Original: This paper studies Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space ( namely, a Borel right process (BRP)) and the pricing kernel ( stochastic discount factor , state-price density ) is a positive semimartingale multiplicative functional of X.
Revised: This paper studies Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space ( namely, a Borel right process (BRP)) and the pricing kernel ( stochastic discount factor (SDF ) is a positive semimartingale multiplicative functional of X.
Edit intent: clarity