wanyu/IteraTeR_full_sent huggingface dataset:
Original: A study of the boundedness in probability of the set of possible wealth outcomes of an economic agent facing constraints, and with limited access to information , is undertaken. The wealth-process set is abstractly structured with reasonable economic properties, instead of the usual practice of taking it to consist of stochastic integrals against a semimartingale integrator.
Revised: A study of the boundedness in probability of the set of possible wealth outcomes of an economic agent facing constraints, and with limited access to information . The set of wealth processes available to the agent is structured with reasonable economic properties, instead of the usual practice of taking it to consist of stochastic integrals against a semimartingale integrator.
Edit intent: clarity
Original:  We obtain the equivalence of (a) the boundedness in probability of  wealth outcomes with (b) the existence of at least one deflator that make the deflated wealth processes have a generalized supermartingale property.
Revised:  We obtain the equivalence of the boundedness in probability of wealth outcomes with (b) the existence of at least one deflator that make the deflated wealth processes have a generalized supermartingale property.
Edit intent: fluency
Original:  We obtain the equivalence of (a) the boundedness in probability of  wealth outcomes with (b) the existence of at least one deflator that make the deflated wealth processes have a generalized supermartingale property.
Revised:  We obtain the equivalence of (a) the boundedness in probability of the set of terminal wealth outcomes with (b) the existence of at least one deflator that make the deflated wealth processes have a generalized supermartingale property.
Edit intent: meaning-changed
Original:  We obtain the equivalence of (a) the boundedness in probability of  wealth outcomes with (b) the existence of at least one deflator that make the deflated wealth processes have a generalized supermartingale property.
Revised:  We obtain the equivalence of (a) the boundedness in probability of wealth outcomes with the existence of at least one deflator that make the deflated wealth processes have a generalized supermartingale property.
Edit intent: clarity
Original:  We obtain the equivalence of (a) the boundedness in probability of  wealth outcomes with (b) the existence of at least one deflator that make the deflated wealth processes have a generalized supermartingale property.
Revised:  We obtain the equivalence of (a) the boundedness in probability of wealth outcomes with (b) the existence of at least one strictly positive deflator that makes the deflated wealth processes have a generalized supermartingale property.
Edit intent: meaning-changed
Original:  We obtain the equivalence of the boundedness in probability of the set of terminal wealth outcomes  with the existence of at least one strictly positive deflator that makes the deflated wealth processes have a generalized supermartingale property.
Revised:  We obtain the equivalence of the boundedness in probability of the set of terminal wealth outcomes (which in turn is equivalent to the weak market viability condition of absence of arbitrage of the first kind) with the existence of at least one strictly positive deflator that makes the deflated wealth processes have a generalized supermartingale property.
Edit intent: meaning-changed
Original:  In particular, they are global indices, that is they do not preserve any %DIFDELCMD < {\em %%% local information about the performance dynamics either in time or for a particular investment horizon.
Revised:  In particular, they are global indices, that is they do not preserve any %DIFDELCMD < {\em %%% 'local' information about the performance dynamics either in time or for a particular investment horizon.
Edit intent: clarity
Original:  Moreover, we {\it   show that the inter-transmission probability undergoes a dramatic change at \gamma_0=1/m^2 and falls into two qualitatively distinct categories: either approximately Gaussian or {\it L\'evy} \alpha-stable distribution with \alpha \in (1,2) entailing infinite variances, {\it leaning} tendency, and {\it directional} unfairness.
Revised:  Moreover, we identify the{\it show that the inter-transmission probability undergoes a dramatic change at \gamma_0=1/m^2 and falls into two qualitatively distinct categories: either approximately Gaussian or {\it L\'evy} \alpha-stable distribution with \alpha \in (1,2) entailing infinite variances, {\it leaning} tendency, and {\it directional} unfairness.
Edit intent: meaning-changed
Original:  Moreover, we {\it   show that the inter-transmission probability undergoes a dramatic change at \gamma_0=1/m^2 and falls into two qualitatively distinct categories: either approximately Gaussian or {\it L\'evy} \alpha-stable distribution with \alpha \in (1,2) entailing infinite variances, {\it leaning} tendency, and {\it directional} unfairness.
Revised:  Moreover, we {\it long-range dependence show that the inter-transmission probability undergoes a dramatic change at \gamma_0=1/m^2 and falls into two qualitatively distinct categories: either approximately Gaussian or {\it L\'evy} \alpha-stable distribution with \alpha \in (1,2) entailing infinite variances, {\it leaning} tendency, and {\it directional} unfairness.
Edit intent: meaning-changed
Original:  Moreover, we {\it   show that the inter-transmission probability undergoes a dramatic change at \gamma_0=1/m^2 and falls into two qualitatively distinct categories: either approximately Gaussian or {\it L\'evy} \alpha-stable distribution with \alpha \in (1,2) entailing infinite variances, {\it leaning} tendency, and {\it directional} unfairness.
Revised:  Moreover, we {\it in 802.11 and show that the inter-transmission probability undergoes a dramatic change at \gamma_0=1/m^2 and falls into two qualitatively distinct categories: either approximately Gaussian or {\it L\'evy} \alpha-stable distribution with \alpha \in (1,2) entailing infinite variances, {\it leaning} tendency, and {\it directional} unfairness.
Edit intent: meaning-changed
Original:  We first make a simplistic Palm interpretation of the Bianchi's formula and on the basis of which, succinct equations describing the backoff distribution as a function of the collision probability \gamma are derived, which also correct a possible misunderstanding in the field. The observation that the entropy of the backoff process in 802.11 increases with the number of nodes leads us to see through a Poissonian character inherent in 802.11. However, it is also found that the collision effect between nodes prevails over the Poissonian aggregation effect in spite of its tendency to increase with the number of nodes. Based on these findings, we formulate the principle about the inter-transmission probability that lays a foundation for the short-term fairness analysis. Another principle discovered upon regular variation theory is that the backoff times have a truncated Pareto-type tail distribution with an exponent of (\log \gamma)/\log m (m is the multiplicative factor  ).
Revised:  A simplistic principle founded upon regular variation theory is that the backoff times have a truncated Pareto-type tail distribution with an exponent of (\log \gamma)/\log m (m is the multiplicative factor ).
Edit intent: coherence
Original:  Another principle discovered upon regular variation theory is that the backoff times have a truncated Pareto-type tail distribution with an exponent of (\log \gamma)/\log m (m is the multiplicative factor  ).
Revised:  Another principle discovered upon regular variation theory is that the backoff time has a truncated Pareto-type tail distribution with an exponent of (\log \gamma)/\log m (m is the multiplicative factor ).
Edit intent: fluency
Original:  Another principle discovered upon regular variation theory is that the backoff times have a truncated Pareto-type tail distribution with an exponent of (\log \gamma)/\log m (m is the multiplicative factor  ).
Revised:  Another principle discovered upon regular variation theory is that the backoff times have a truncated Pareto-type tail distribution with an exponent of (\log \gamma)/\log m (m is the multiplicative factor and \gamma is the collision probability ).
Edit intent: meaning-changed
Original:  This reveals that the  backoff process is heavy-tailed in the strict sense for m^2 \gamma>1 , essentially due to collision. Moreover, we identify long-range dependence in 802.11 through both of mathematical and empirical wavelet-based analyses and answer a riddle: the absence of long range dependence in aggregate total load.
Revised:  This reveals that the backoff process is heavy-tailed in the strict sense for m^2 \gamma>1 /m^2, and paves the way for the following unifying result. The state-of-the-art theory on the superposition of the heavy-tailed processes is applied to establish a dichotomy exhibited by the aggregate backoff process, putting emphasis on the importance of time-scale on which we view the backoff processes. While the aggregation on normal time-scales leads to a Poisson process, it is approximated by a new limiting process possessing long-range dependence in 802.11 through both of mathematical and empirical wavelet-based analyses and answer a riddle: the absence of long range dependence in aggregate total load.
Edit intent: meaning-changed
Original:  Moreover, we identify long-range dependence in 802.11 through both of mathematical and empirical wavelet-based analyses and answer a riddle: the absence of long range dependence in aggregate total load.
Revised:  Moreover, we identify long-range dependence (LRD) on coarse time-scales. This dichotomy turns out to be instrumental in formulating short-term fairness, extending existing formulas to arbitrary population, and to elucidate the absence of long range dependence in aggregate total load.
Edit intent: meaning-changed
Original:  Moreover, we identify long-range dependence in 802.11 through both of mathematical and empirical wavelet-based analyses and answer a riddle: the absence of long range dependence in aggregate total load. We also show that the inter-transmission probability undergoes a dramatic change at \gamma_0=1/m^2 and falls into two qualitatively distinct categories: either approximately Gaussian or L\'evy \alpha-stable distribution with \alpha \in (1,2) .
Revised:  Moreover, we identify long-range dependence in 802.11 through both of mathematical and empirical wavelet-based analyses and answer a riddle: the absence of LRD in practical situations. A refined wavelet analysis is conducted to strengthen this argument .
Edit intent: clarity
Original:  A universal effect in ensembles of similar systems under  load of similar factors is described: in crisis, typically, even before obvious symptoms of crisis appear, correlation increases, and, at the same time, variance (and volatility) increases too.
Revised:  A universal effect in ensembles of similar systems under the load of similar factors is described: in crisis, typically, even before obvious symptoms of crisis appear, correlation increases, and, at the same time, variance (and volatility) increases too.
Edit intent: fluency
Original: We consider the problem of option pricing under stochastic volatility models, focusing on the  two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein.
Revised: We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein.
Edit intent: meaning-changed
Original:  We show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the expressions of the characteristic function and the first four cumulants for the risk neutral probability measure.
Revised:  Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the expressions of the characteristic function and the first four cumulants for the risk neutral probability measure.
Edit intent: coherence
Original:  We show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the expressions of the characteristic function and the first four cumulants for the risk neutral probability measure.
Revised:  We show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the exact expression of the characteristic function and the first four cumulants for the risk neutral probability measure.
Edit intent: clarity
Original:  We show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the expressions of the characteristic function and the first four cumulants for the risk neutral probability measure. This allows us to obtain a semi-closed form for European option prices , based on Lewis ' approach.
Revised:  We show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the expressions of the characteristic function and the first four cumulants for the risk neutral probability density. Its knowledge allows us to obtain a semi-closed form for European option prices , based on Lewis ' approach.
Edit intent: clarity
Original:  This allows us to obtain a semi-closed form for European option prices , based on Lewis ' approach. We deeply analyze the case of Plain Vanilla calls, being liquid instruments for which reliable implied volatility surfaces are available.
Revised:  This allows us to compute option prices exploiting Lewis and Lipton formula. We analyze in detail the case of Plain Vanilla calls, being liquid instruments for which reliable implied volatility surfaces are available.
Edit intent: meaning-changed
Original: The questions in the experimental and theoretical research in the field of interaction of weak influences of various fields with biological objects in conditions when an intense of the influence is smalland weak perturbation are analyzed.
Revised: The effect of ultralow-frequency or static magnetic and electric fields on biological processes is of huge interest for researchers due to the resonant change of the intensity of biochemical reactions although the energy in such fields is small. A simplified model to study the effect of the weak magnetic and electrical fields on fluctuation of the influence is smalland weak perturbation are analyzed.
Edit intent: meaning-changed
Original: The questions in the experimental and theoretical research in the field of interaction of weak influences of various fields with biological objects in conditions when an intense of the influence is smalland weak perturbation are analyzed. The type of resonant interactions connected with these processes is considered. The new method of decision of the k_BT problem in magnetobiology is offered.
Revised: The questions in the experimental and theoretical research in the field of interaction of weak influences of various fields with biological objects in conditions when an intense of the random ionic currents in blood and to solve the k_BT problem in magnetobiology is offered.
Edit intent: meaning-changed
Original:  The new method of decision of the k_BT problem in magnetobiology is offered. On the basis of results of the previous work arXiv:0904.1198%DIFDELCMD < ] %%% the analytical expression of energy of a molecule in considered area has been obtained.
Revised:  The new method of decision of the k_BT problem in magnetobiology is arXiv:0904.1198%DIFDELCMD < ] %%% the analytical expression of energy of a molecule in considered area has been obtained.
Edit intent: clarity
Original:  On the basis of results of the previous work arXiv:0904.1198%DIFDELCMD < ] %%% the analytical expression of energy of a molecule in considered area has been obtained. Numerical estimations of the energy of molecules in capillary and aorta volume are resulted: for the values of relaxation rate \Lambda=0.5 \lambda, 0.05 \lambda, and 0.005 \lambda we obtain the energies \varepsilon=2, 20 and 200 k_BT, respectively, for the molecules of capillaries and \varepsilon=2\cdot 10^{-9} , 20\cdot 10^{-9, and 200\cdot 10^{-9} k_BT, respectively, for the molecules of the aorta.
Revised:  On the basis of results of the previous work arXiv:0904.1198%DIFDELCMD < ] %%% suggested. The analytic expression for the kinetic energy of the molecules dissolved in certain liquid media is obtained. The values of the magnetic field leading to resonant effects in capillaries are estimated. The numerical estimates showed that the resonant values of the energy of molecular in the capillaries and aorta are different: under identical conditions a molecule of the aorta gets 10^{-9} , 20\cdot 10^{-9, and 200\cdot 10^{-9} k_BT, respectively, for the molecules of the aorta.
Edit intent: meaning-changed
Original:  Numerical estimations of the energy of molecules in capillary and aorta volume are resulted: for the values of relaxation rate \Lambda=0.5 \lambda, 0.05 \lambda, and 0.005 \lambda we obtain the energies \varepsilon=2, 20 and 200 k_BT, respectively, for the molecules of capillaries and \varepsilon=2\cdot 10^{-9} , 20\cdot 10^{-9, and 200\cdot 10^{-9} k_BT, respectively, for the molecules of the aorta.
Revised:  Numerical estimations of the energy of molecules in capillary and aorta volume are resulted: for the values of relaxation rate \Lambda=0.5 \lambda, 0.05 \lambda, and 0.005 \lambda we obtain the energies \varepsilon=2, 20 and 200 k_BT, respectively, for the molecules of capillaries and \varepsilon=2\cdot 10^{-9} , and 200\cdot 10^{-9} k_BT, respectively, for the molecules of the aorta.
Edit intent: fluency
Original:  The }  capillaries are very sensitive to the resonance effectand the average energy of the molecule localized in the capillary is increased by several orders of magnitude as compared to its thermal energy .
Revised:  The } times less energy than the molecules in blood capillaries. So the capillaries are very sensitive to the resonance effectand the average energy of the molecule localized in the capillary is increased by several orders of magnitude as compared to its thermal energy .
Edit intent: meaning-changed
Original:  The }  capillaries are very sensitive to the resonance effectand the average energy of the molecule localized in the capillary is increased by several orders of magnitude as compared to its thermal energy .
Revised:  The } capillaries are very sensitive to the resonant effect, with an approach to the resonant value of the magnetic field strength, the average energy of the molecule localized in the capillary is increased by several orders of magnitude as compared to its thermal energy .
Edit intent: meaning-changed
Original:  The }  capillaries are very sensitive to the resonance effectand the average energy of the molecule localized in the capillary is increased by several orders of magnitude as compared to its thermal energy . This value of the energy is sufficient for the deterioration of the chemical bonds .
Revised:  The } capillaries are very sensitive to the resonance effectand the average energy of the molecule localized in the capillary is increased by several orders of magnitude as compared to its thermal energy , this value of the energy is sufficient for the deterioration of the chemical bonds .
Edit intent: fluency
Original:  We give a necessary and sufficient condition for the process Z to be a true martingale in the case where M_t=\int_0^t b(Y_u)  dW_u and Y is a one-dimensional diffusion driven by a Brownian motion ~ W. Furthermore, we provide a necessary and sufficient condition for Z to be a uniformly integrable martingale in the same setting.
Revised:  We give a necessary and sufficient condition for the process Z to be a true martingale in the case where M_t=\int_0^t b(Y_u) \, dW_u and Y is a one-dimensional diffusion driven by a Brownian motion ~ W. Furthermore, we provide a necessary and sufficient condition for Z to be a uniformly integrable martingale in the same setting.
Edit intent: coherence
Original:  We give a necessary and sufficient condition for the process Z to be a true martingale in the case where M_t=\int_0^t b(Y_u)  dW_u and Y is a one-dimensional diffusion driven by a Brownian motion ~ W. Furthermore, we provide a necessary and sufficient condition for Z to be a uniformly integrable martingale in the same setting.
Revised:  We give a necessary and sufficient condition for the process Z to be a true martingale in the case where M_t=\int_0^t b(Y_u) dW_u and Y is a one-dimensional diffusion driven by a Brownian motion W. Furthermore, we provide a necessary and sufficient condition for Z to be a uniformly integrable martingale in the same setting.
Edit intent: fluency
Original:  These conditions are deterministic and expressed only in terms of the function b and the drift and diffusion coefficients of ~ Y. As an application we provide a deterministic criterion for the absence of bubbles in a one-dimensional setting.
Revised:  These conditions are deterministic and expressed only in terms of the function b and the drift and diffusion coefficients of Y. As an application we provide a deterministic criterion for the absence of bubbles in a one-dimensional setting.
Edit intent: fluency
Original: We prove existence and uniqueness of stochastic equilibria in a representative class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and general  random endowments.
Revised: We prove existence and uniqueness of stochastic equilibria in a class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and general random endowments.
Edit intent: clarity
Original: We prove existence and uniqueness of stochastic equilibria in a representative class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and general  random endowments.
Revised: We prove existence and uniqueness of stochastic equilibria in a representative class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and general Markovian random endowments.
Edit intent: meaning-changed
Original:  In both models we calculate discounted cumulative dividend payments until the ruin time  .
Revised:  In both models we calculate discounted cumulative dividend payments until the ruin time . This paper is an attempt at understanding the effect of dependencies of two portfolios on the the join optimal strategy of paying dividends. For the proportional reinsurance we can observe for example the interesting phenomenon that is dependence of choice of the optimal barrier on the initial reserves. This is a contrast to the one-dimensional Cram\'{e .
Edit intent: meaning-changed
Original:  For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of O(\log n) and \Omega(\log n/\log\log n) for \alpha=2 and \Theta(n^{ 1-\alpha/ 2  }) for \alpha<2 respectively.
Revised:  For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of O(\log n) and \Omega(\log n/\log\log n) for \alpha=2 and \Theta(n^{ 2 }) for \alpha<2 respectively.
Edit intent: meaning-changed
Original:  For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of O(\log n) and \Omega(\log n/\log\log n) for \alpha=2 and \Theta(n^{ 1-\alpha/ 2  }) for \alpha<2 respectively.
Revised:  For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of O(\log n) and \Omega(\log n/\log\log n) for \alpha=2 and \Theta(n^{ 1-\alpha/ 2 /\alpha-1 }) for \alpha<2 respectively.
Edit intent: meaning-changed