Truncated variation - its properties and applications in stochastic

... Remark The rate of convergence in (8) is better than the rate of the usual algorithms based on the calendar time or business time sampling (this was proved at least for some class of diffusions), and is of the same order as the order of tick time sampling schemes, which are special case of stochasti ...

... Remark The rate of convergence in (8) is better than the rate of the usual algorithms based on the calendar time or business time sampling (this was proved at least for some class of diffusions), and is of the same order as the order of tick time sampling schemes, which are special case of stochasti ...

Elements of Information Theory Second Edition Solutions to Problems

... Each weighing has three possible outcomes - equal, left pan heavier or right pan heavier. Hence with k weighings, there are 3 k possible outcomes and hence we can distinguish between at most 3k different “states”. Hence 2n + 1 ≤ 3k or n ≤ (3k − 1)/2 . Looking at it from an information theoretic view ...

... Each weighing has three possible outcomes - equal, left pan heavier or right pan heavier. Hence with k weighings, there are 3 k possible outcomes and hence we can distinguish between at most 3k different “states”. Hence 2n + 1 ≤ 3k or n ≤ (3k − 1)/2 . Looking at it from an information theoretic view ...

On Generalized Measures of Information with

... The opportunity to watch Dr. Shalabh Bhatnagar in action (particularly during discussions) has fashioned my way of thought in problem solving. He has been a valuable adviser, and I hope my three and half years of working with him have left me with at least few of his qualities. I am thankful to the ...

... The opportunity to watch Dr. Shalabh Bhatnagar in action (particularly during discussions) has fashioned my way of thought in problem solving. He has been a valuable adviser, and I hope my three and half years of working with him have left me with at least few of his qualities. I am thankful to the ...

Measure Theoretic Probability P.J.C. Spreij (minor revisions by S.G.

... The notes are used during a course that had as one of its principal aims a swift introduction to measure theory as far as it is needed in modern probability, e.g. to define concepts as conditional expectation and to prove limit theorems for martingales. Everyone with a basic notion of mathematics an ...

... The notes are used during a course that had as one of its principal aims a swift introduction to measure theory as far as it is needed in modern probability, e.g. to define concepts as conditional expectation and to prove limit theorems for martingales. Everyone with a basic notion of mathematics an ...

Measure Theoretic Probability P.J.C. Spreij

... The notes are used during a course that had as one of its principal aims a swift introduction to measure theory as far as it is needed in modern probability, e.g. to define concepts as conditional expectation and to prove limit theorems for martingales. Everyone with a basic notion of mathematics an ...

... The notes are used during a course that had as one of its principal aims a swift introduction to measure theory as far as it is needed in modern probability, e.g. to define concepts as conditional expectation and to prove limit theorems for martingales. Everyone with a basic notion of mathematics an ...

The Curious Case of Noninteractive Commitments

... {0, 1}n which f (x) is accepted by the circuit. It is easy to see that a random oracle is a hitting oneway function with overwhelming probability (see Lemma 5.2). Furthermore, we show that there exists a non-black-box construction of non-interactive commitments from hitting one-way functions as foll ...

... {0, 1}n which f (x) is accepted by the circuit. It is easy to see that a random oracle is a hitting oneway function with overwhelming probability (see Lemma 5.2). Furthermore, we show that there exists a non-black-box construction of non-interactive commitments from hitting one-way functions as foll ...

NBER WORKING PAPER SERIES FINANCIAL ASSET RETURNS, DIRECTION-OF-CHANGE FORECASTING, AND VOLATILITY DYNAMICS

... sign forecast is correct.2 This leads Levich, for example, to focus on what he terms useful forecasts, namely those that predict the direction of price change and hence “...lead to profitable speculative positions and correct hedging decisions.” Interestingly, there is substantial evidence that sign ...

... sign forecast is correct.2 This leads Levich, for example, to focus on what he terms useful forecasts, namely those that predict the direction of price change and hence “...lead to profitable speculative positions and correct hedging decisions.” Interestingly, there is substantial evidence that sign ...

Multi-Verifier Signatures

... public-key signatures to a secret-key setting with a signer and multiple verifiers, each using different keys. We also provide two efficient MVS constructions: • Atomic Signatures requires the signer to solve a system of linear equations. As far as we know, Atomic Signatures constitutes the first pr ...

... public-key signatures to a secret-key setting with a signer and multiple verifiers, each using different keys. We also provide two efficient MVS constructions: • Atomic Signatures requires the signer to solve a system of linear equations. As far as we know, Atomic Signatures constitutes the first pr ...

pdf

... random tapes, respectively, in run r, ρr is an additional tape whose role is explained in Section 3, and P ∗ and V ∗ are the protocols of the prover and verifier. An interactive protocol (P, V ) generates a system. The runs of the system correspond to possible executions of (P, V ). Following HMT, ...

... random tapes, respectively, in run r, ρr is an additional tape whose role is explained in Section 3, and P ∗ and V ∗ are the protocols of the prover and verifier. An interactive protocol (P, V ) generates a system. The runs of the system correspond to possible executions of (P, V ). Following HMT, ...

Probability Essentials. Springer, Berlin, 2004.

... Gauss (1777–1855), and Laplace (1749–1827). For a nice history of Probability before 1827 (the year of the death of Laplace) one can consult [21]. In the twentieth century it was Kolmogorov (1903–1987) who saw the connection between the ideas of Borel and Lebesgue and probability theory and he gave ...

... Gauss (1777–1855), and Laplace (1749–1827). For a nice history of Probability before 1827 (the year of the death of Laplace) one can consult [21]. In the twentieth century it was Kolmogorov (1903–1987) who saw the connection between the ideas of Borel and Lebesgue and probability theory and he gave ...

# Ars Conjectandi

Ars Conjectandi (Latin for The Art of Conjecturing) is a book on combinatorics and mathematical probability written by Jakob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way, and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations—the aforementioned problems from the twelvefold way—as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.