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The " elliptic " version of a three-dimensional nonlinear integrable equation, the Toda chain equation, is studied by means of the inverse scattering method. Several classes of decaying solutions corresponding to both the continuous and discrete spectrum of the associated spectral problem are obtained. Conditions that guarantee reality and analyticity along… (More)
By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same… (More)
In this paper we obtain general conditions under which stochastic differential equations possess a strong solution representable in an explicit form as a functional of the Wiener process. Particular interest bears the problem of determining conditions that guarantee non-explosion of the solution. The necessary as well as sufficient condition is derived.
78 end formation modeling, 2) intelligent architectural systems, and 3) emerging technologies and materials; each has a different logic and enhances design in various ways. The goal is to prepare students to help further the field of architecture by introducing these evolving design methods. The architecture school teaches the fundamentals of creative… (More)
We consider the fair martingale prize of insurance contracts with benefit received either at the insurer's demise or at maturity. We show how to modify the dynamics of the underlying so as to incorporate the possibility that the traded stock has a strong support at some level. The resulting dynamics is integrated and the fair prize of several natural… (More)
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary time by recourse to renewal theory. The… (More)
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related in a certain way we show that our model can be integrated in an exact way. The related problem of how to prize general… (More)