We generalize the method of obtaining fundamental linear partial differential equations such as the diffusion and Schrodinger equation, the Dirac, and the telegrapher's equation from a simple stochastic consideration to arrive at a certain nonlinear form of these equations. A group classification through a one-parameter group of transformations for two of these equations is also carried out.

The goal of this paper is to clarify for which starting points the state processes of a stochastic partial differential equation with an affine realization are time-homogeneous. We will illustrate our results by means of the HJMM equation from mathematical finance.

We extend the narrowband Weyl symbol (WS) and the wideband P0-Weyl symbol (P0WS) for dispersive time–frequency (TF) analysis of nonstationary random processes and time-varying systems. We obtain the new TF symbols using unitary transformations on the WS and the P0WS. For example, whereas the WS is matched to systems with constant or linear TF characteristics, the new symbols are better matched ...

We consider the evolution of a passive scalar in a shear flow in its representation as a system of lattice differential equations in wave number space. When the velocity field has small support, the interaction in wave number space is local and can be studied in terms of dispersive linear lattice waves. We close the restriction of the system to a finite set of wave numbers by implementing trans...

We give a concise introduction to risk sensitive control of Markov diffusion processes and related two-controller, zero-sum differential games. The method of dynamic programming for the risk sensitive control problem leads to a nonlinear partial differential equation of HamiltonJacobi-Bellman type. In the totally risk sensitive limit, this becomes the Isaacs equation for the differential game. ...

5 [1] We study the influence of buoyancy and spatial heterogeneity on the spreading of the 6 saturation front of a displacing fluid during injection into a porous medium saturated 7 with another, immiscible fluid. To do so we use a stochastic modeling framework. We 8 derive an effective large‐scale flow equation for the saturation of the displacing fluid that 9 is characterized by six nonlocal ...

In this paper, a class C1 of risk measures, which generalizes the class of risk measures for the right-tail deviation suggested by Wang (1998), is characterized in terms of dispersive order. If dispersive order does not hold, unanimous comparisons are still possible by restricting our attention to a subclass C2 ⊂ C1 and then the criterion is the excess wealth order. Sufficient conditions for st...

Über die statistische Beschreibung nichtstationärer Mobilfunkkanäle. In diesem Artikel wird die statistische Beschreibung von Mobilfunkkanälen behandelt, welche nicht die Annahme schwach stationärer unkorrelierter Streuer erfüllen. Besondere Beachtung hierbei findet die lokale Streufunktion. Die vorgestellten Methoden, welche besonders für schwach dispersive und schwach korrelierte Kanäle geeig...

We present a new dispersive analysis of the isospin breaking decay η → 3π. The resulting representation of the decay amplitude allows us to determine the quark mass double ratio Q and we find as a preliminary result Q = 22.3 ± 0.4. Finally, we discuss a number of improvements that we intend to implement in the future.