Results 1  10
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14
The Russian Option: Reduced Regret
, 1993
"... this paper the value of the option (i.e. the supremum in (1.2)) will be found exactly, and in particular it will be shown that the maximum in (1.2) is finite if and only if r ? ¯ : (1.4) Assuming (1.4), an explicit formula is given for both the maximal expected present value and the optimal stopping ..."
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Cited by 36 (2 self)
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this paper the value of the option (i.e. the supremum in (1.2)) will be found exactly, and in particular it will be shown that the maximum in (1.2) is finite if and only if r ? ¯ : (1.4) Assuming (1.4), an explicit formula is given for both the maximal expected present value and the optimal stopping rule in (2.4), which is not a fixed time rule but depends heavily on the observed values of X t and S t . We call the financial option described above a "Russian option" for two reasons. First, this name serves to (facetiously) differentiate it from American and European options, which have been extensively studied in financial economics, especially with the new interest in market economics in Russia. Second, our solution of the stopping problem (1.2) is derived by the socalled principle of smooth fit, first enunciated by the great Russian mathematician, A. N. Kolmogorov, cf. [4, 5]. The Russian option is characterized by "reduced regret" because the owner is paid the maximum stock price up to the time of exercise and hence feels less remorse at not having exercised at the maximum. For purposes of comparison and to emphasize the mathematical nature of the contribution here, we conclude the paper by analyzing an optimal stopping problem for the Russian option based on Bachelier's (1900) original linear model of stock price fluctuations, X
On the shape of the ground state eigenvalue density of a random Hill’s equation
 Comm. Pure Appl. Math
, 2006
"... Consider the Hill’s operator Q = −d 2 /dx 2 +q(x) in which q(x), 0 ≤ x ≤ 1, is a White Noise. Denote by f(µ) the probability density function of −λ0(q), the negative of the ground state eigenvalue, at µ. We prove the detailed asymptotics: f(µ) = 4 µ exp ..."
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Cited by 4 (3 self)
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Consider the Hill’s operator Q = −d 2 /dx 2 +q(x) in which q(x), 0 ≤ x ≤ 1, is a White Noise. Denote by f(µ) the probability density function of −λ0(q), the negative of the ground state eigenvalue, at µ. We prove the detailed asymptotics: f(µ) = 4 µ exp
Threshold effects in parameter estimation as phase transitions in statistical mechanics
 IEEE Trans. Inf. Theory
"... Threshold effects in the estimation of parameters of non–linearly modulated, continuous– time, wideband waveforms, are examined from a statistical physics perspective. These threshold effects are shown to be analogous to phase transitions of certain disordered physical systems in thermal equilibriu ..."
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Cited by 3 (2 self)
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Threshold effects in the estimation of parameters of non–linearly modulated, continuous– time, wideband waveforms, are examined from a statistical physics perspective. These threshold effects are shown to be analogous to phase transitions of certain disordered physical systems in thermal equilibrium. The main message, in this work, is in demonstrating that this physical point of view may be insightful for understanding the interactions between two or more parameters to be estimated, from the aspects of the threshold effect. Index Terms: Non–linear modulation, parameter estimation, threshold effect, additive white Gaussian noise channel, bandwidth, statistical physics, disordered systems, random energy
ON EQUIVALENCE OF PROBABILITY MEASURES
, 1970
"... Let H be a real and separable Hilbert space, f the Borel afield of H sets, and III and ll2 two probability measures on (H,r). III and 1J2 are equivalent (mutually absolutely continuous) 1f, for Aef, 1J 1(A) = = 0 <=> 1J2 (A) = = o. Several sufficient conditions for equivalence are obtained in this ..."
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Cited by 2 (0 self)
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Let H be a real and separable Hilbert space, f the Borel afield of H sets, and III and ll2 two probability measures on (H,r). III and 1J2 are equivalent (mutually absolutely continuous) 1f, for Aef, 1J 1(A) = = 0 <=> 1J2 (A) = = o. Several sufficient conditions for equivalence are obtained in this paper. Some of these results do not require that III and 112 be Gaussian. The conditions obtained are applied to show equivalence for some spec1fic measures when H is L
Absolute continuity between the Wiener and Stationary Gaussian Measures. preprint
, 1998
"... Abstract. It is known that the entropy distance between two Gaussian measures is finite if, and only if, they are absolutely continuous with respect to one another. Shepp [5] characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to t ..."
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Cited by 1 (1 self)
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Abstract. It is known that the entropy distance between two Gaussian measures is finite if, and only if, they are absolutely continuous with respect to one another. Shepp [5] characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to the Wiener measure. By analyzing the entropy distance, we show that one of his conditions, involving the spectrum of an associated operator, is essentially extraneous, providing a simple criterion for finite entropy distance in this case. 1. introduction Let C[1 − τ,1+τ] (where 0 <τ<1) denote the space of continuous functions on [1 − τ,1+τ]. A standard Brownian motion observed between times 1 − τ and 1 + τ induces on C[1 − τ,1+τ] the Wiener measure W τ. As a Gaussian measure, it is characterized by its correlation R(t, s) =t ∧ s for t, s ∈ [1 − τ,1+τ], and by its vanishing mean. A Gaussian measure, Q τ,onC[1 − τ,1+τ]isstationary if its mean is constant and its correlation is a Töeplitz function. That is, with X ∈ C[1 − τ,1+τ] being the sample path, and µt
2005): On the equivalence of multiparameter Gaussian processes
 Journal of Theoretical Probability
"... Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a s ..."
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Cited by 1 (1 self)
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Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a special type of stochastic equation with linear noise.
ZeroOne Laws for Multiple Stochastic Integrals
, 1994
"... In this paper we study zeroone laws for processes represented as finite sums of stochastic integrals with respect to symmetric infinitely divisible random measures. We survey known results on zeroone laws for infinitely divisible measures and for polynomial Gaussian and type G chaos with values ..."
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In this paper we study zeroone laws for processes represented as finite sums of stochastic integrals with respect to symmetric infinitely divisible random measures. We survey known results on zeroone laws for infinitely divisible measures and for polynomial Gaussian and type G chaos with values in abstract measurable spaces. We then prove a new zeroone law for processes represented as finite sums of multiple integrals under a certain assumption of atomlessness on the L'evy measure. We further study the question of whether the "center" of such processes belongs to a space if the process itself does. Most important applications of our results are to sample path properties of stochastic processes represented as sums of stochastic integrals. 1 Introduction and notation This paper deals with stochastic integrals with respect to infinitely divisible random measures , and we start with properly introducing this object. Let (E; E) be a measurable space, and let G be a ffiring o...
Optimal RedA QuadAClassifiers Using the FukunagaKoontz Transform, with Applications to Automated Target Recognition
, 2003
"... In target recogni2BU appli2BU; of di;U;A2BU t or classiA2BU; analysi2 each `feature'i s a result of a convoluti; of aniAD#R wi a filter,whi h may bederi ed from a feature vector. Iti si ortant to userelati ely few features. We analyze anoptiO; reducedrank classiRA under the twoclass si ..."
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In target recogni2BU appli2BU; of di;U;A2BU t or classiA2BU; analysi2 each `feature'i s a result of a convoluti; of aniAD#R wi a filter,whi h may bederi ed from a feature vector. Iti si ortant to userelati ely few features. We analyze anoptiO; reducedrank classiRA under the twoclass siqBqqqA2 AssumiD each populati2 i Gaussi and has zero mean, and the classes diqB through the covari#SR matriRA2 # 1 and # 2 . The followil matrii consiR#qUA #=(# 1 +# 2 ) 1/2 # 1 (# 1 +# 2 ) 1/2 .
Institute of Statistics Mimeo Series No. 865 March, 1973EQUIVALENT GAUSSIAN MEASURES WHOSE RN DERIVATIVE IS THE EXPONENTIAL OF
"... for any purpose of the ..."
Some Remarks on the Equivalence of Gaussian Processes
, 1973
"... s · AU THORIS) (FI,st name, middle inltla'. 'ast na",e) ..."