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A linear operator acting in a Hilbert space and defined on the whole space is called completely continuous if it maps bounded sets into relatively compact sets (a set is
Walsh’s theory of martingale measures in order to deal with stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation,
We define the first passage bridge from 0 to λ as the Brownian motion on the time interval [0,1] conditioned to first hit λ at time 1. We show that this process may be related to
The inequality (2) holds also for the more general setting of locally square integrable (continuous-parameter) martingales with bounded jumps (c.f. right-continuous with
The main purpose of this article is to study the symmetric martingale property and capacity defined by G-expectation introduced by Peng (cf. We show that the G-capacity can not
So, using the martingale property of M we see that N is a local martingale. The equivalence between i) and ii) in the above proposition corresponds to a well known
The key point is to exploit the strong parallel between the new technique introduced by Bass and Perkins [2] to prove uniqueness of the martingale problem in the framework
Using the auto-B¨ acklund transformations of the continuous Painlev´e equations we derive their contiguity relations which are just the quantum forms for the discrete P I , P II , P