Alexander Novikov

On some maximal inequalities for fractional Brownian motions

We prove some maximal inequalities for fractional Brownian motions. These extend the Burkholder-Davis-Gundy inequalities for fractional Brownian motions. The methods are based on the integral representations of fractional Brownian motions with respect to a certain Gaussian martingale in terms of beta kernels.

On a solution of the optimal stopping problem for processes with independent increments

We discuss a solution of the optimal stopping problem for the case when a reward function is a power function of a process with independent stationary increments (random walks or Levy processes) on an infinite time interval. It is shown that an optimal stopping time is the first crossing time through a level defined as the largest root of the Appell function associated with the maximum of the underlying process.

Sequential estimation of the parameters of diffusion processes

For the parameter λ of a diffusion processξ(t), satisfying the stochastic differential equation dξ(t)=λf (t,ξ)dt+dw(l), we propose an effective sequential estimation plan with an unbiased and normally distributed estimate. The proposed sequential plan is discussed in detail for the example of a process ξ(t) having a linear stochastic differential.

Optical properties and efficient laser oscillation at 2066 nm of novel Tm:Lu 2 O 3 ceramics

Structural, optical, and spectroscopic properties of novel Tm3+:Lu2O3 ceramics are studied. The average grain size is determined to be ~0.54-0.56 μm. The absorption spectra show good opportunities for diode pumping at 796 nm and 811 nm. The ceramics have high mid-IR transmittance of up to 7 μm. Strong luminescence lines are measured at 1942 nm, 1965 nm, and 2066 nm. CW laser operation at 2066 nm with an output power of up to 26 W and a slope efficiency of 42% is obtained. Q-switched operation with a pulse duration of 100-150 ns and a repetition rate of 5-10 kHz is achieved.

On fair pricing of emission-related derivatives

Tackling climate change is at the top of many agendas. In this context, emission trading schemes are considered as promising tools. The regulatory framework for an emission trading scheme introduces a market for emission allowances and creates a need for risk management by appropriate financial contracts. In this work, we address logical principles underlying their valuation.

Martingales and First-Passage Times for Ornstein-Uhlenbeck Processes with a Jump Component

Using martingale technique, we show that a distribution of the first-passage time over a level for the Ornstein--Uhlenbeck process with jumps is exponentially bounded. In the case of absence of positive jumps, the Laplace transform for this passage time is found. Further, the maximal inequalities are also given when the marginal distribution is stable.

Low-inductance multigap spark modules

We outline the design concept for low-inductance high-current spark modules at a voltage level of 100 kV and a current of 1 MA. We present the results of an investigation of the switching and operating characteristics of multichannel, multigap spark modules as a function of the design and the shape and amplitude of the beam pulse. We give a description of the designs and parameters of the developed types of spark modules.

Bayesian Sequential Estimation of a Drift of Fractional Brownian Motion

Abstract We solve explicitly a Bayesian sequential estimation problem for the drift parameter μ of a fractional Brownian motion under the assumptions that a prior density of μ is Gaussian and that a penalty function is quadratic or Dirac-delta. The optimal stopping time for this case is deterministic.

Martingales and first passage times of AR(1) sequences

Using the martingale approach we find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences. Further, we prove a martingale identity to be used in obtaining explicit bounds for the expectation of first passage times.

A Structural Model with Unobserved Default Boundary

A firm‐value model similar to the one proposed by Black and Cox (1976) is considered. Instead of assuming a constant and known default boundary, the default boundary is an unobserved stochastic process. This process has a Brownian component, reflecting the influence of uncertain effects on the precise timing of the default, and a jump component, which relates to abrupt changes in the policy of the company, exogenous events or changes in the debt structure. Interestingly, this setup admits a default intensity, so the reduced form methodology can be applied. Part of this work was done while the first author stayed at the Isaac Newton Institute in Cambridge. Financial support from Isaac Newton Institute and Deutsche Forschungsgemeinschaft is gratefully acknowledged. The authors would like to thank M. Davis, L.C.G. Rogers, K. Giesecke and T. Bjrk for their inspiring comments and Ling Xu for her excellent help with the simulations. Moreover, the authors are grateful to N. Kordzakhia and two anonymous referees for their suggestions which helped to improve the paper considerably.