Recursos de colección

Hokkaido University Collection of Scholarly and Academic Papers (135.521 recursos)

HUSCAP (Hokkaido University Collection of Scholarly and Academic Papers) contains peer-reviewed journal articles, proceedings, educational resources and any kind of scholarly works of Hokkaido University.

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Mostrando recursos 1 - 20 de 43

  1. On the equations of stationary processes with divergent diffusion coefficients

    Inoue, Akihiko
    We investigate a class of Langevin equations with delay. The random noises in the equations are adopted so that they are in accordance with linear response theory in statistical physics. We prove that every purely nondetermistic, stationary Gaussian process with divergent diffusion coefficients as well as reflection positivity is characterized as the unique solution of one of such equations. This extends the results of Okabe to processes with divergent diffusion coefficients. A correspondence between the decays of the delay coefficient of the equation and the correlation function of the solution is obtained. We see that it is of different type...

  2. Integrable four-vortex motion on sphere with zero moment of vorticity

    Sakajo, Takashi
    We consider the motion of N vortex points on sphere, called the N-vortex problem, which is a Hamiltonian dynamical system. The three-vortex problem is integrable and its motion has already been resolved. On the other hand, when the moment of vorticity vector, which consists of weighed sums of the vortex positions, is zero at the initial moment, the four-vortex problem is integrable, but it has not been investigated yet. The present paper gives a description of the integrable four-vortex problem with the reduction method to a three-vortex problem used by Aref and Stremler. Moreover, we examine whether the vortex points...

  3. Tauberian and Mercerian Theorems for Systems of Kernels

    Bingham, N. H.; Inoue, A.

  4. Financial Markets with Memory II: Innovation Processes and Expected Utility Maximization

    Anh, V.; Inoue, A.; Kasahara, Y.
    We develop a prediction theory for a class of processes with stationary increments. In particular, we prove a prediction formula for these processes from a finite segment of the past. Using the formula, we prove an explicit representation of the innovation processes associated with the stationary increments processes. We apply the representation to obtain a closed-form solution to the problem of expected logarithmic utility maximization for the financial markets with memory introduced by the first and second authors.

  5. Linear filtering of systems with memory and application to finance

    Inoue, A.; Nakano, Y.; Anh, V.
    We study the linear filtering problem for systems driven by continuous Gaussian processes V(1) and V(2) with memory described by two parameters. The processes V(j) have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. They allow for straightforward parameter estimations. After giving the semimartingale representations of V(j) by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the optimal portfolio problem for an investor with partial observations. We illustrate the tractability of the filtering algorithm by numerical implementations.

  6. Extension of the Drasin-Shea-Jordan theorem

    BINGHAM, Nicholas H.; INOUE, Akihiko
    Passing from regular variation of a function f to regular variation of its integral transform k*f of Mellin-convolution form with kernel k is an Abelian problem; its converse, under suitable Tauberian conditions, is a Tauberian one. In either case, one has a comparison statement that the ratio of f and k*f tends to a constant at infinity. Passing from a comparison statement to a regular-variation statement is a Mercerian problem. The prototype results here are the Drasin-Shea theorem (for non-negative k) and Jordan's theorem (for k which may change sign). We free Jordan's theorem from its non-essential technical conditions which...

  7. Asymptotic behavior for partial autocorrelation functions of fractional ARIMA processes

    Inoue, Akihiko
    We prove a simple asymptotic formula for partial autocorrelation functions of fractional ARIMA processes.

  8. On the worst conditional expectation

    Inoue, Akihiko
    We study continuous coherent risk measures on Lp, in particular, the worst conditional expectations. We show some representation theorems for them, extending the results of Artzner, Delbaen, Eber, Heath, and Kusuoka.

  9. Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing

    Inoue, Akihiko; Kasahara, Yukio
    Let {Xn : ∈Z} be a fractional ARIMA(p,d,q) process with partial autocorrelation function α(·). In this paper, we prove that if d∈(−1/2,0) then |α(n)|~|d|/n as n→∞. This extends the previous result for the case 0

  10. Financial Markets with Memory I: Dynamic Models

    Anh, V.; Inoue, A.
    This is the first of two papers in which we consider a stock with price process defined by a stochastic differential equation driven by a process Y(·) different from Brownian motion. The adoption of such a colored noise input is motivated by an analysis of real market data. The process Y(·) is defined by a continuous-time AR(∞)-type equation and may have either short or long memory. We show that the process Y(·) has a good MA(∞)-type representation. The existence of such simultaneous good AR(∞) and MA(∞) representations enables us to apply a new method for the calculation of relevant conditional...

  11. Explicit representation of finite predictor coefficients and its applications

    Inoue, Akihiko; Kasahara, Yukio
    We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof is based on the alternate applications of projection operators associated with the infinite past and the infinite future. Applying the result to long memory processes, we give the rate of convergence of the finite predictor coefficients and prove an inequality of Baxter-type.

  12. A prediction problem in L2(w)

    Pourahmadi, Mohsen; Inoue, Akihiko; Kasahara, Yukio
    For a nonnegative integrable weight function w on the unit circle T, we provide an expression for p = 2, in terms of the series coefficients of the outer function of w, for the weighted Lp distance inff ∫T |1 − f|pwdμ,| where μ is the normalized Lebesgue measure and f ranges over trigonometric polynomials with frequencies in [{. . . ,−3,−2,−1}\{−n}]∪{m}, m ≥ 0, n ≥ 2. The problem is open for p ≠2.

  13. Binary market models with memory

    Inoue, Akihiko; Nakano, Yumiharu; Anh, Vo
    We construct a binary market model with memory that approximates a continuous-time market model driven by a Gaussian process equivalent to Brownian motion. We give a sufficient condition for the binary model to be arbitrage-free. In a case when arbitrage opportunities exist, we present the rate at which the arbitrage probability tends to zero.

  14. Optimal Long-Term Investment Model with Memory

    Inoue, Akihiko; Nakano, Yumiharu
    We consider a financial market model driven by an Rn-valued Gaussian process with stationary increments which is different from Brownian motion. This driving-noise process consists of n independent components, and each component has memory described by two parameters. For this market model, we explicitly solve optimal investment problems. These include: (i) Merton's portfolio optimization problem; (ii) the maximization of growth rate of expected utility of wealth over the infinite horizon; (iii) the maximization of the large deviation probability that the wealth grows at a higher rate than a given benchmark. The estimation of parameters is also considered.

  15. Double Commuting Compressed Shifts and Generalized Interpolation in the Hardy Space over the Bidisk

    Nakazi, Takahiko; Seto, Michio
    This paper deals with an operator theory of compressed shifts on the Hardy space over the bidisk. We give commutant lifting type theorems and some interpolation theorems in two variables.

  16. Unirationality of certain supersingular K3 surfaces in characteristic 5

    Duc, Tai Pho; Shimada, Ichiro
    We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational.

  17. 書評「T. Kaczynski, K. Mischaikow, and M. Mrozek:Computational Homology (Applied Mathematical Sciences 157, Springer-Verlag, 2004 年, 480 ページ)」

    平岡, 裕章; 坂上, 貴之

  18. Efficient and fast numerical methods to compute fluid flows in the geophysical β plane

    SAKAJO, T.

  19. On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities

    Cho, Yonggeun; Kim, Hyunseok
    We study the Navier-Stokes equations for compressible barotropic fluids in a bounded or unbounded domain Ω of R^3. We first prove the local existence of solutions (ρ,u) in C([0,T_*]; (ρ^∞ + H^3(Ω)) × D^1_0 ∩ D^3)(Ω)) under the assumption that the data satisfies a natural compatibility condition. Then deriving the smoothing effect of the velocity u in t > 0, we conclude that (ρ,u) is a classical solution in (0,T_**) × Ω for some T_** ∈ (0,T_*]. For these results, the initial density needs not be bounded below away from zero and may vanish in an open subset (vacuum) of...

  20. A particle-field Hamiltonian in relativistic quantum electrodynamics

    Arai, Asao
    We mathematically analyze a Hamiltonian Hτ(V,g) of a Dirac particle—a relativistic charged particle with spin 1/2—minimally coupled to the quantized radiation field, acting in the Hilbert space F:=[⊕^4^L^2(R^3)]⊗ F rad, where F rad is the Fock space of the quantized radiation field in the Coulomb gauge, V is an external potential in which the Dirac particle moves, g is a photon-momentum cutoff function in the interaction between the Dirac particle and the quantized radiation field, and τ∈R is a deformation parameter connecting the Hamiltonian with the "dipole approximation" (τ=0) and the original Hamiltonian (τ=1). We first discuss the self-adjointness problem...

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