Search results for "Bounds"
showing 10 items of 298 documents
On an approximation problem for stochastic integrals where random time nets do not help
2006
Abstract Given a geometric Brownian motion S = ( S t ) t ∈ [ 0 , T ] and a Borel measurable function g : ( 0 , ∞ ) → R such that g ( S T ) ∈ L 2 , we approximate g ( S T ) - E g ( S T ) by ∑ i = 1 n v i - 1 ( S τ i - S τ i - 1 ) where 0 = τ 0 ⩽ ⋯ ⩽ τ n = T is an increasing sequence of stopping times and the v i - 1 are F τ i - 1 -measurable random variables such that E v i - 1 2 ( S τ i - S τ i - 1 ) 2 ∞ ( ( F t ) t ∈ [ 0 , T ] is the augmentation of the natural filtration of the underlying Brownian motion). In case that g is not almost surely linear, we show that one gets a lower bound for the L 2 -approximation rate of 1 / n if one optimizes over all nets consisting of n + 1 stopping time…
On the gonality and the slope of a fibered surface
2018
Abstract Let f : X → B be a locally non-trivial relatively minimal fibration of curves of genus g ≥ 2 . We obtain a lower bound of the slope λ ( f ) increasing with the gonality of the general fiber of f. In particular, we show that λ ( f ) ≥ 4 provided that f is non-hyperelliptic and g ≥ 16 .
Learning small programs with additional information
1997
This paper was inspired by [FBW 94]. An arbitrary upper bound on the size of some program for the target function suffices for the learning of some program for this function. In [FBW 94] it was discovered that if “learning” is understood as “identification in the limit,” then in some programming languages it is possible to learn a program of size not exceeding the bound, while in some other programming languages this is not possible.
Descriptional and Computational Complexity of the Circuit Representation of Finite Automata
2018
In this paper we continue to investigate the complexity of the circuit representation of DFA—BC-complexity. We compare it with nondeterministic state complexity, obtain upper and lower bounds which differ only by a factor of 4 for a Binary input alphabet. Also we prove that many simple operations (determining if a state is reachable or if an automaton is minimal) are PSPACE-complete for DFA given in circuit representation.
Upper bounds on multiparty communication complexity of shifts
1996
We consider some communication complexity problems which arise when proving lower bounds on the complexity of Boolean functions. In particular, we prove an \(O(\frac{n}{{2\sqrt {\log n} }}\log ^{1/4} n)\)upper bound on 3-party communication complexity of shifts, an O(n e ) upper bound on the multiparty communication complexity of shifts for a polylogarithmic number of parties. These bounds are all significant improvements over ones recently considered “unexpected” by Pudlak [5].
On the propagation of a perturbation in an anharmonic system
2007
We give a not trivial upper bound on the velocity of disturbances in an infinitely extended anharmonic system at thermal equilibrium. The proof is achieved by combining a control on the non equilibrium dynamics with an explicit use of the state invariance with respect to the time evolution.
AIs for Dominion Using Monte-Carlo Tree Search
2015
Dominion is a complex game, with hidden information and stochastic elements. This makes creating any artificial intelligence AI challenging. To this date, there is little work in the literature on AI for Dominion, and existing solutions rely upon carefully tuned finite-state solutions. This paper presents two novel AIs for Dominion based on Monte-Carlo Tree Search MCTS methods. This is achieved by employing Upper Confidence Bounds UCB and Upper Confidence Bounds applied to Trees UCT. The proposed solutions are notably better than existing work. The strongest proposal is able to win 67% of games played against a known, good finite-state solution, even when the finite-state solution has the u…
Warrant Exercise and Bond Conversion in Large Trader Economies
2006
It is well known that the sequential (premature) exercise of American-type warrants may be advantageous for large warrantholders, even in the absence of regular dividends, because using exercise proceeds to repurchase stock or to expand the firm's scale increases the riskiness of an equity share. We present an upper bound on this advantage and show that this advantage is negligible for a realistic parameter setting. This result, however, does not justify in general the simplifying restriction that warrants or convertible securities are valued as if exercised as a block. It turns out that the option to exercise only a fraction of the outstanding convertibles at the maturity date (partial exe…
Rotational coherence imaging and control for CN molecules through time-frequency resolved coherent anti-Stokes Raman scattering
2011
Numerical wave packet simulations are performed for studying coherent anti-Stokes Raman scattering (CARS) for CN radicals. Electronic coherence is created by femtosecond laser pulses between the X²Σ and B²Σ states. Due to the large energy separation of vibrational states, the wave packets are superpositions of rotational states only. This allows for a specially detailed inspection of the second- and third-order coherences by a two-dimensional imaging approach. We present the time-frequency domain images to illustrate the intra- and intermolecular interferences, and discuss the procedure to rationally control and experimentally detect the interferograms in solid Xe environment. peerReviewed
Sobolev and bounded variation functions on metric measure spaces
2014
International audience