
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...

Sakajo, Takashi
We consider the motion of N vortex points on sphere, called the Nvortex problem, which is a Hamiltonian dynamical system. The threevortex 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 fourvortex problem is integrable, but it has not been investigated yet. The present paper gives a description of the integrable fourvortex problem with the reduction method to a threevortex problem used by Aref and Stremler. Moreover, we examine whether the vortex points...

Bingham, N. H.; Inoue, A.

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 closedform solution to the problem of expected logarithmic utility maximization for the financial markets with memory introduced by the first and second authors.

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 KalmanBucytype 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.

BINGHAM, Nicholas H.; INOUE, Akihiko
Passing from regular variation of a function f to regular variation of its integral transform k*f of Mellinconvolution 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 regularvariation statement is a Mercerian problem. The prototype results here are the DrasinShea theorem (for nonnegative k) and Jordan's theorem (for k which may change sign). We free Jordan's theorem from its nonessential technical conditions which...

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

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.

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

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 continuoustime 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...

Inoue, Akihiko; Kasahara, Yukio
We consider the finitepast 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 Baxtertype.

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 − fpwdμ, 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.

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

Inoue, Akihiko; Nakano, Yumiharu
We consider a financial market model driven by an Rnvalued Gaussian process with stationary increments which is different from Brownian motion. This drivingnoise 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.

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.

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

平岡, 裕章; 坂上, 貴之

Cho, Yonggeun; Kim, Hyunseok
We study the NavierStokes 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...

Arai, Asao
Some representationtheoretic aspects of a twodimensional quantum system of a charged particle in a vector potential A, which may be singular on an infinite discrete subset D of R^2 are investigated. For each vector v in a set V(D)⊂ R^2\{0}, the projection Pv of the physical momentum operator P := pαA to the direction of v is defined by Pv := v・P as an operator acting in L^2(R^2), where p = (iDx,iDy)[(x,y)∈ R^2] with Dx (resp., Dy) being the generalized partial differential operator in the variable x (resp., y) and α∈ R is a parameter denoting the charge of the...

Arai, Asao
A twodimensional quantum system of a charged particle interacting with a vector potential determined by the Weierstrass Zeta function is considered. The position and the physical momentum operators give a representation of the canonical commutation relations with two degrees of freedom. If the charge of the particle is not an integer (the case corresponding to the Aharonov–Bohm effect), then the representation is inequivalent to the Schrödinger representation. It is shown that the inequivalent representation induces infinitedimensional Hilbert space representations of the quantum group Uq(sl2). Some properties of these representations of Uq(sl2) are investigated.