1555430
On a general class of one-factor models for the term structure of interest rates

Abstract.We propose a general one-factor model for the term structure of interest rates which based upon a model for the short rate. The dynamics of the short rate is described by an appropriate function of a time-changed Wiener process. The model allows for perfect fitting of given term structure of interest rates and volatilities, as well as for mean reversion. Moreover, every type of distribution of the short rate can be achieved, in particular, the distribution can be concentrated on an interval. The model includes several popular models such as the generalized Vasicek (or Hull-White) model, the Black-Derman-Toy, Black-Karasinski model, and others. There is a unified numerical approach to the general model based on a simple lattice approximation which, in particular, can be chosen as a binomial or 
$N$-nomial lattice with branching probabilities 
$1/N$.

120009511
On semimartingale diffusions and stochastic differential equations
Given a regular diffusion X on the real axis which is a semimartingale we describe the semimartingale decomposition of X. We then give necessary and sufficient conditions in terms of the scale and the speed measure for X being a solution of an Ito type stochastic differential equation driven by a Wiener process and with classical drift or a drift term involving the local time of X. A regular diffusion is also characterized as unique solution of a certain martingale problem. Finally we discuss an example related to skew Brownian motion
121309269
Stochastic Integration for Some Rough Non‐adapted Processes
For the Wiener process W on the unit interval and 0 ⩽ θ ⩽ 1/4 consider the non-adapted process ut =sgn(Wt−θ)sgn(W1−WT+θ), θ⩽t⩽1−θ. By giving explicit descriptions of their expansions in terms of generalized Hermite polynomials we show that they possess Skorohod integral processes. In the more interesting case θ = 0, a component due to the interaction of forwards and backwards Wiener process seems to dominate the non-interaction part, whereas for θ > 0 interaction drops geometrically with respect to non-interaction. We translate these purely analytic properties into more familiar terms of samples of stochastic processes. Firstly, we construct simple approximations of the integral process which are of the type of Riemann sums. We then show that their quadratic variations are the same as for the Wiener process on [θ, 1 − θ]. Finally, using the fact that W remains a semimartingale if its filtration is enlarged by W1, we compare the resulting Ito integral process to the Skorohod integral process of u in case θ = 0. We show that they differ by a local time. Consequently the Skorohod integral process of u is a semimartingale.
120957526
On Stochastic Differential Equations with Reflecting Barriers
122911860
Quantentheorie der Felder als Distributionstheorie
ZusammenfassungDie Distributionstheorie vonL. Schwartz wird zu einer mathematisch konsistenten Formulierung der Quantenfeldtheorie verwendet. Die Einführung von Distributionen impliziter Funktionen gestattet es, viele Formeln mit geringfügigen Änderungen in den strengen Formalismus zu übernehmen. Die Annahme, daß es eine raumzeitliche Feldoperatordistribution gibt, führt auf einen vonWigiitman angegebenen Hilbertraum. Er ist durch eine Folge von Distributionen, die Vakuumerwartungswerte der Theorie, bestimmt. Diese werden für die freien Felder (Schrödinger-Gordon-Feld, Maxwellfeld, Diracfeld) aus einfachen Annahmen hergeleitet. Beim Maxwellfeld ergibt sich zwanglos, daß die Metrik nur in dem durch die Lorentzbedingung eingeschränkten Hilbertraum definit ist. Die Definition einer Dichte-Distribution, welche den üblichen Doppelpunktprodukten entspricht, erweist sich auch in dieser Fassung der Quantenfeldtheorie als möglich.RiassuntoViene applicata la teoria delle distribuzioni diL. Schwartz nella formulazione della teoria quantistica dei campi onde risulti matematicamente consistente. L’introduzione di funzioni di distribuzione permette di ottenere moite formule nel formalismo rigoroso e con cambiamenti semplicissimi rispetto alla formulazione corrente. Facendo l’ipotesi dell’esistenza di un operatore di campo spazio-temporale avente l’aspetto distribuzionale, si arriva alla formulazione di uno spazio Hilbertiano introdotto dalWightman: taie spazio è metricamente definite da una suecessione di distribuzioni le quali altro non sono che i valori medi del vuoto risultanti dalla teoria. Tali valori vengono ottenuti con semplici ipotesi per i campi di Schrödinger-Gordon, di Maxwell, di Dirac. A proposito del campo elettromagnetico si osaerva che la metrica è definita solo in un sottospazio dell’intero spazio di Hilbert definito dalla condizione di Lorentz. Infine si rende possibile la definizione di densità di corrente nella struttura della teoria, densità che corrisponde all’abituale.
121073876
Existence of solutions of certain nonconvex optimal control problems governed by nonlinear integral equations
Optimal control problems with nonlinear equations usually do not have a solution, i.e. an optimal control. Nevertheless, if the cost functional is uniformly concave with respect to the state, the solution may exist. Using the Balder's technique based on a Youngmeasure relaxation, Bauer's external principle and investigation of extreme Young measures; the existence is demonstrated here for optimal control processes described by nonlinear integral equations
123201234
Badly approximable systems of linear forms
A number α is called badly approximable if there is a constant c = c(α)>0 such that 
|q|αq − p| > c(α) 
for any integers p, q ≠ 0. The existence of continuum—many badly approximable numbers follows easily from the theory of continued fractions. In the present paper the notion of a badly approximable number is generalized to badly approximable systems of m linear forms in n variables. Among other results we prove for every given m and n the existence of continuum many badly approximable systems of linear forms.
121422615
Flächenapproximation beim Jacobialgorithmus
123904692
Simultaneous Approximation to a Basis of a Real Numberfield
0 < aXq + pi C(q) (1?i?n). It is known [1,4] that N(h;a, * ,a.,,) is for almost all (al,* *,an) in the sense of Lebesgue asymptotically equal to * (h) for large h. Hence one would expect this to be true of many given n-tuples, say of (7r', P,e). One would be more hesitant to expect this of (/31<, * ,8,l/) if 1, I *,n is a basis of a real numberfield of degree n + 1, because of the exceptional status of such n-tuples in diophantine approximations. In fact, N(h;l, ; / , 83n) =0 for all h if gf(q) = cq-lln and 0 < c < c0(P1y . ,,3n). But the asymptotic formula does hold under a further mild assumption on t(q): THEOREM 1. Let J(q), 1(h) be as before, and assume that